All Solutions - Snow Pyramids - January 8-12, 1996
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Correct solutions were submitted by:
Atlantic City HS, Atlantic City, New Jersey Zack Subin, Grade 9 Bethel Park High School, Bethel Park, Pennsylvania Peter DeFilippo, Grade 11 Bishop Walsh Middle/HS, Frederick, Maryland Timothy Farrell, Grade 10 Camden-Rockport High School, Camden, Maine Jim Hamalainen, Grade 10 College Park High School, Pleasant Hill, Kyaw Soe Mon (Kay), Melissa Brown, Grade 9 Garfield High School, Seattle, Washington Benjamin Warfield, Grade 12 Gov. Thomas Johnson High, Frederick, Maryland Russell Rector, Grade 12 Hinckley-Finlayson HS, Hinckley, Minnesota Sarah Dagget, Grade 11 Angie Clark & Joanna Olson, Grade 10 Juneau-Douglas High School, Juneau, Alaska Cody Bennett, Grade 9 Mount St. Joseph Academy, Flourtown, Pennsylvania Grade 10 Colleen Cusick, Luisa Galdi & Kristi Giballa, Jenn Cody, Susan McGowan, Claire Bonner & Christina Niescier Grade 9 Katie Walder , Amy Barbieri & Celine McElwee, Liz Croney, Melissa DiFeo, Lindsay Pio, Lauren Wall & Lindsay Parsons, Jackie Benn & Shannon Firth, Michele Weiss & Jackie Mattera Murray Junior High School, Ridgecrest, California Cassie Gorish, Grade 8 Thomas S. Kuo, Grade 7 Newport High School, Bellevue, Washington Irene Chin, Grade 9 Pamlico County HS, Bayboro, North Carolina Pashuan Armond, Matt Ottinger, Grade 10 Roselle Park High School, Roselle Park, New Jersey Christine Guercio, Grade 9 Smoky Hill High School, Aurora, Colorado Scott Golembeski, Michael Bancroft, Brian Christenson, Grade 9 Amber & Meagan, Brian McCloskey, Grade 10 Wauconda High School, Wauconda, Illinois George Baird, Grade ? Westwood Jr. Sr. High School, Westwood, New Jersey Mathew, Grade 8 Wydown Middle School, Clayton, Missouri Antonina Frolova, Grade 7 And the post-high school crew: Ken Duisenberg, Post-Master's, California State University, Chico Brian Gordon, Dartmouth '92, Middletown, Connecticut Jon Tan, DLSU, Philippines
Submitted by Jim Hamalainen Step 1. Convert all lengths or amounts into inches or cubic inches. 1 mile= 63360 inches and 50 yrds.= 1800 inches Step 2. Find total amount of snow collected by plow. (length times width times height) 63360" x 1800" x 30" = 3,421,440,000 cubic inches of snow. Step 3. Divide snow volume into four even amounts (for 4 pyramids) = 855,360,000 cubic inches of snow per pyramid Step 4. To find height, assume that there is snow filling in space above the present pyramid in such a way to form a rectangular prism. The volume of this "box" would be three times the amount of one pyramid, or 2,566,080,000 cubic inches of snow. Step 5. Divide the volume of the "box" by the base area of the pyramid (which is 1800" x 1800"= 3,240,000 square inches) to find the height of the pyramid. The final answer is 22 yrds tall (or 66 ft or 792 inches tall). ***************************************************** From: Timothy Farrell Grade: Sophomore (10) School: Bishop Walsh Middle/High School Answer: 50 yards x 1 mile x 30 inches= 150 feet x 5280 feet x 2.5 feet= 1980000 feet^3 He made four pyramids each exactly the same, so we'll just take 1/4 of the above height to simplify the situation. .25x1980000 feet^3=495000 feet^3 Pyramid volume formula: area of base x height/3 area of base= 50 yd ^2= 150 feet x 150 feet= 22500 feet^2 Volume of pyramid: Let n=height of each pyramid 22500 feet^2 x (n feet)/3=495000 feet^3 22500 feet^2 x (n feet)/3x3=495000 feet^3x3 22500 feet^2 x (n feet)=1485000 feet^3 22500 feet^2 / 22500 feet^2 x (n feet)=1485000 feet^3/22500 feet ^2 (n feet)=66 feet Therefore, the size of the pyramid is: 50 yards wide x 50 yards long x 66 feet (22 yards) tall ********************************************* From: Scott Golembeski Grade: 9 School: Smokey Hill High School Answer: each pyramid is 22 yards tall because the formula for figuring out the volume of a pyramid is 1/3 base times height, so the base is 2,500 so when you figure it all out it comes out to be 22 yards. ********************************************* From: Amber and Meagan Grade: 10 School: shhs Answer: The height of the pyramid will be 22 yards tall. ********************************************* From: Brian McCloskey Grade: 10 School: shhs Answer: Each pyramid would be 22 yards tall because the formula for determining the height of a pyramid is area divided by base. That is the formula that I used to get my humble answer. ********************************************* From: Cassie Gorish Grade: 8 School: Murray Junior High Answer: This is my answer for the question: First, I went into the Smithsonian Institute on the Internet and looked up the Great Pyramid of Giza. Using this information, I could make a proportion, but I chose another way. With my dad, I looked up in his Mechanical Engineer Manual the equation for finding the volume of pyramids. By finding the volume of the snow the man plowed and dividing it into four, I can find the volume of each pyramid: I found the volume to be 495,000 cubic feet. The equation for finding the volume of pyramids is: V = 1/3 height X area of the base Since I know the volume and the base length, I can solve for height: 495000 = 1/3 h X 22500 22 = 1/3 h 66 = height So, assuming that he built all the pyramids of equal dimensions, each pyramid is 66 feet in height. ********************************************* From: Michael Bancroft Grade: 9 School: Smoky Hill High Answer: Hello once again Annie, I have figured it out. The answer is 22 yards tall. I suppose that I have to tell you how I got it, so: After drawing a picture of the snowcovered runway, and marking the measurements in feet. Dividing 5,280' into 4 (total number of prymids) I got 1320' and found the volume of the rectangle. Dallas Clayborne and I were working on this, so we got the same thing. Using the equation v=1/3 area of bxh we kept on getting 66. Mrs. Sandler told us that the answer was 22, so we did it over and over, and then it hit me, that is 66 feet, and the answer should be in yards, so 66' = 22 yards!! ********************************************* From: Cody Bennett Grade: 9th School: JDHS (Phoenix) Answer: 66 Feet tall To solve this puzzling problem I first calculated the volume of snow that I was dealing with, which was 1,980,000 cu. ft. Next I found the base area of the pyramids, which was 22500 sq. ft. After that I then divided the total snow by four so that I would know how much snow went into each pyramid. This number was 495,000 cu. ft. I then multiplied this number by 3 because I know that B*H/3 was the area of each pyramid and I was trying to simplify the equation. The result of this was 1,485,000. I divided this by the previously found base of 22,500 sq. ft. to come up with the answer of 66 feet tall. Below I have included some of the things that I found useful. 30"=2.5' 2.5*150*5280=1980000 sq ft of snow total 1980000/4=amount of snow per pyramid=495000 495000*3=b*h=1485000 b=22500 1485000/b=66 base 22500 sq ft 4 pyramids 1,980,000 cu. ft. of snow 66 feet tall ********************************************* Solution from George Baird (copied exactly by his teacher) Wauconda High School Wauconda, Il. 60084 First you find the volume of the rectangle that was 50 yd x 1 mile x 30 " which equaled 440000/6 cu yds. Then divide that by 4, because there are 4 pyramids, which leaves you with 440000/24. Next you have to use the volume pyramid equation, v= Bh/3. To get B ( the area of the base). You take 50 x 50 = 2500. Now you know v=440000/24 and B = 2500, so put them in the equation and solve for h, which is the height of the pyramid. When you're done, you'll find the pyramid is 22 yds high. ********************************************* From: Antonina Frolova Grade: 7 School: Wydown Middle School, Clayton, MO Answer: This is the formula I used: h=3abc/(yz^2) a=width of space being plowed in feet b=length of space being plowed in feet c=hight of snow on the ground in feet y=how many pyramids were build z^2=area of base of pyramid (z length of side in feet) h=height of pyramid in feet 3 is coefficient from the formula for the volume of a pyramid 3*150*5280*2.5/(4*50^2)=66 The height of the pyramid is 66 feet ********************************************* Dear Annie, We converted 1 mile to 1,760 yds, and 30 in. to 5/6 yds. Then to find v, we multiplied 1760, 5/6, and 50 yds to get 73,333.333. Take that number and divide by four to get 18,333.333 of each pyramid. That's volume. Subsitute that into the formula of v=1/3area of base*h. Take the area of the base triangle which is 2500. Put all that in and you get 22 as your height. Pashuan Armond Pamlico County High School ********************************************* From: Thomas S. Kuo School: Murray Junior High School, Ridgecrest, California Grade: 7th The height of the pyramids is 22 yards. I figured this out by using the equation, 4 times bh/3, b standing for base which is 50 x 50 and h standing for height (bh/3 is the volume of a pyramid and assume that all 4 pyramids have the same height), is equal to 30" times 50 yards times 1 mile. I changed all of these units to yards so it is 4 times bh/3 is equal to 5/6 yards times 50 yards times 1760 yards. I solved for h and ended up with the answer 22 yards. 4 x (bh/3) = 30" x 50 yards x 1 mile 4 x (50 x 50 x h /3) = 5/6 x 50 x 1760 h = 22 yards ********************************************* First I converted all the information to yards. I ended up with 73,333.333 repeating yards to make four pyramids. I divide by four. 18333.333=1/3 X area of base X height Area of base equals 2500 yards, and the pyramids were 22 yards high. Matt Ottinger Pamlico County High School Bayboro, NC ********************************************* From: Christine Guercio Grade: 9 School: ROSELLE PARK HIGH SCHOOL Answer: First I found the volume of the parking lot. I had to convert all the measurments into yards and then used the formula for the volume of the parking lot (length x width x height). This gave me 73333 1/3 as the volume and I divided it by four because this snow went into four pyramids. After dividing by four I got 18333 1/3. The formula for the volume of a pyramid is 1/3 area of the base x height = volume. I found the area of the base to be 2500 and divided it by three. I got 833 1/3. I put these numbers into the formula and solved for height. 833 1/3 x h = 18333 1/3 The height equaled 22 yds or 66 ft. ********************************************* The volume of a pyramid is 1/3Bh. The are of the square base in feet^2 is 150 square or 22500. Divide that by 3 and you get 7500. Multiply that by four, because of the four pyramids, and you get 3o,000. That number times your height will give you the total volume of the snow. The volume of the snow in square feet is 5280*150*2.5=1980000 The mile was converted to 5280, 50 yeards to 150, and 30 inches to 2.5. 1,980,000 divided by 30,000=66 which is your answer. The pyramids are 66 feet high. Peter DeFilippo Bethel Park PA Grade 11 ********************************************* We're trying it again. Our first answer was 198 yds. This time we got 22 yds. We tried it in feet instead of yards and it came out better (don't know why). We found the volume of snow to be 495,000 cubic feet. Our equation looked like 495,000 = 1/3(22,500)h. The 22500 came from multiplying 150ft x 150ft. Our answer came out to be 66 ft. We divided by 3 and converted to yards. 22 yards seems a little more reasonable! Angie Clark Joanna Olson Hinckley-Finlayson H.S. ********************************************* Hi! My name is Sarah Dagget. I am from Hinckley/Finlayson H.S. I am a junior. My Solution for the prolem of the week was 22 yards high for each of the four pyramids. I got this solution by using the formula for the volume of a pyramid ( v = 1/3 * B * h ). First I arranged the equation so that I was solving for h (height), h = v/(1/3 * B ). Then I figured out the volume of all the snow ( V = s*s*h ) (50*1760*5/6). To make all the measurements equal I converted them all to yards. After I figured out the Volume of the snow,73333 1/3, I figured out B ( the surface area of the snow being plowed ) by taking 50 * 1760 . That was equal to 2500. Then I plugged all the information to the equation so it went... 73333 1/3 / ( 1/3 * 2500) that was equal to 88. That was the height of one triangle and so the plower was making four pyramid I divided 88 by 4 and got 22yds. That was my answer. ********************************************* From: Brian Christenson Grade: 9 School: SHHS Answer: To find the answer, first I converted everything to feet. I then found the volume of the area that needed to be plowed, and divided that by 4 to get the volume of each pyramid, which is 495,000. Then I found the area of each base, and got 22,500. I then applied th formula: v= 1/3 B*h. The heigth of each pyramid is 22 yards. ********************************************* Irene Chin, Grade 9, Newport High School PROCEDURE: 1.) Find total area of snow: (2.5)(150)(5280)=1,980,000 feet 2.) Divide by 4 (four pyramids) 1,980,000/4=495,000 3.) Formula for square pyramids V=bh/3 So, (150)(150)h/3=495,000 4.) h=66 The height of each pyramid is 66 feet or 22 yards. ********************************************* From: MATHEW Grade: 8 School: Westwood Jr. Sr. Highschool The Formula for volume of a pyramid is Volume=1/3*base area*height. To start I decided to figure everything in inches to avoid decimals. 1 mile is 63360 inches 50 yards is 1800 inches. Then the total volume of snow is 63360 * 1800 * 30 = 3421440000 cubic inches. 3421440000 is then devided by 4 and you get 855360000 cubic inches per pyramid. For base area the 50 yards or 1800" is used and you get a base area of 3240000". The formula is then put together as 855360000 = 1/3 * 3240000 * height. That makes the height 792 inches or 22 YARDS TALL. ********************************************* From: Russell Rector Grade: 12 School: Gov. Thomas Johnson High Answer: 2.5'*150'*5280'=.25*(1/3)*(150^2)*h h=66' The first time I didn't convert the base to feet. The second time I didn't use the correct formula for volume of a pyramid. ********************************************* Katie Walder Mount Saint Joseph Academy Grade 9 This problem seemed very complicated at the beginning, but I think I figured it out. The area the guy was plowing was a 3-dimensional rectangle. I labeled its length as a mile, or 5,280 feet. I labeled its width as 50 yards, or 150 feet. I labeled its height as 30 inches, or 2.5 feet. I then plugged all my numbers into the formula for the volume of a rectangular prism, as follows: V= (l) x (w) x (h) V= (5280) x (150) x (2.5) V= 1,980,000 cubic feet This is the volume of all the snow, so I divided it by 4 to get the volume of one pyramid, which equalled 495,000. I then used the formula for a pyramid, which is as follows: V = 1/3 Bh 495000 = 1/3 (150 x 150)h 66 = h Each pyramid must then have a height which equals 66 feet, or 22 yards. ********************************************* Kyaw Soe Mon(Kay) 9th grade First of all, I found out the volume of the snow.This is how I did it; Width = 50yds = 150ft. Length = 1 mile = 5280ft. Height= 30in = 2.5ft. 150*5280*2.5= 1,980,000 ft cubed Then I found the volume of 1 pyramid(assuming that all the pyramids are equal): 1,980,000 / 4 = 495,000 ft.cubed. I also know that the area of the base is 150 ft * 150 ft = 22,500 ft squared. I know that the formula for finding the volume of a pyramid is ; Area of base*Height*1/3 , which means Volume of pyramid / Area of base * 3 = Height. Therefore, 495,000/22,500 * 3 = 66ft (or) 33yds. ********************************************* Melissa Brown 9th grade The first thing you want to find is the volume. You would find this by multiplying the 1 mile by the 50 yark width and the 30 inches deep. Because there are so many different units of measure I decided to convert it all to feet. Therefore- 5,280 times 150 feet times 2.5 feet= 1,980,000(the volume of snow) Next you divide by 4, because he made 4 pyramids. 1,980,000 divided by 4= 495,000. Now you find the formula for pyramid volume. This formula says volume =1/3base times height, you already know the volume, 495,000 and the base 22,500 (150 feet times 150 feet) so to find the height you can change the formula around H=3v/B. Height=1,485,000/22,500. This equals 66' inches. Now that you have an answer you can check it in the formula. V=1/3 BH 495,000= 1/3 times 22,500 times 66 495,000= 495,000 66' is correct. ********************************************* From: Zack Subin Grade: 9 School: Atlantic City High School I figured out what my mistake was (I answered 29 1/3 yards). I assumed that the formula for the volume of a pyramid was 1/4Bh, while it is actually 1/3Bh. Thanks for your reply. The answer must be 22 yards. ********************************************* Amy Barbieri & Celine McElwee Mount St Joseph Academy Grade 9 If a guy were to form four perfect square pyramids out of an area of snow 50 yards x 1 mile x 30 inches, we concluded that the height of each pyramid would be 22 yards. We came to this answer through a simple conversion and formula method. First, we converted all of our measurements to yards. We did this because we noticed that a few of the measurements were already in yards. Our measurements for the snow were 50 yards wide, 1,760 yards long, and .83333 yards high. The volume of the area of snow would be 73,333.333 yards, using the formula V=lxwxh. We divided the volume of the snow by 4 because the man made four pyramids out of that snow. We concluded that each pyramid's volume would be 18,333.333 yards. We found that the formula for the volume of a pyramid is V=Bh/3 (B=area of the base). We changed the formula around to equal the height and therefore got the equation h=3V/B. We found the area of the base to be 2500 yards by multiplying 50 yards (one side) by itself, because it is a square. We plugged in our numbers and got h=3x18,333.333/2500. After calculating, we found the height of each pyramid to be 22 yards. ********************************************* Colleen Cusick Mt. St. Joseph Academy Grade 10 This week's problem of the week was to figure out the height of each of the (4) snow pyramids that a snowplower at the Philadelphia Airport creates when he plows a field . The field was 50 yards wide and a mile long, and the snow was 30 inches deep. I decided to use the formulas for volume. I converted all the measurements into yards and then figured out the volume of the field ( it was 73,333 1/3 yards 3) and then divided it by the number of pyramids (4). I got 18,333 1/3 yards3. I then used the formula for the volume of a pyramid ( 1/3 * base 2 * height) with x as height and got 22 yards tall. ********************************************* Luisa Galdi Kristi Giballa Mount Saint Joseph Academy This problem wasn't very difficult, but we had some trouble with the math and conversions. We tried changing the miles and yards to feet or inches , but when we did the calculations, we just ended up confusing ourselves. So, we converted them to yards (50yds. stayed 50yds., 1 mile = 1760yrds., 30in.=5/6yds.). Here's how we came up with our answer. First, we decided we needed to figure out how much snow this guy had to plow. We used the formula for volume (V=lwh). Then we used the information that there would be 4 pyramids and divided the volume by this. We then had the total amount of snow in 1 pyramid. We plugged the information into the formula for the volume of a pyramid (V=Bh/3). B=area of the base, so we found the area of the base of the pyramid by multiplying the length times the width (A of square=s^2 SO A=50^2=2500yds^2). Here's our work in a little more detail. Our final answer was 22yds. high. V=lwh V=(1760)(50)(5/6) V=73333.3yds.^3 73333.3 -------- = 18333.3 4 A=s^2 A=50^2 A=2500yds^2 V=Bh/3 18333.3 = 2500h -------- 3 22yds.=h ********************************************* Liz Croney Mount Saint Joseph Grade9 If four snow pyramids are made and each has a base that is 50 yards by 50 yards, then the height will be 22 yards. I came to this conclusion by first finding the total amount of snow that had to be put into piles. It came out to be 73333 and 1/3yards cubed. Then I divided that by four because there are four piles. I got 18333 and 1/3 yards cubed. After doing that I found the area of the base which was 2500 yards squared. I knew that to find the area of a pyramid you do the area of the base times the height divided by three. I then concluded that the height must be 22 yards because it came out to 18333 and 1/3 yards cubed when I tried it in the equation. ********************************************* Melissa DiFeo Mount St. Joseph Academy Grade 9 The volume of four pyramids = 50 yards x 1 mile x 30 inches. Then you can convert all this into yards , so you can multiply them. To get yards into a mile you get that 5,280 feet are in a mile and divide it by 3 because there are 3 feet in a yard, so there are 1760 yards in a mile to get the amount for inches you divide the amount of inches by the inches per yard. 4 pyramids = 50 yards x 1760 yards x 5/6 yard. Then you simplify everything. 4 pyramids = 73333 1/3 cubic yards 1 pyramid = 73333 1/3 divided by 4 to get that 1 pyramid = 18333 1/3 cubic yards Then you take the formula for volume of a pyramid [ V = 1/3 Bh] and solve for the height. V = 1/3 Bh V = 1/3 [ 50 yards x 50 yards] h Since the volume of 1 pyramid is 18333 1/3 then : 18333 1/3 = 1/3 [ 50 yards x 50 yards ] h 55000/3 = 1/3 [ 50 yards x 50 yards ] h 55000 = 1/3 [50 yards x 50 yards ] h 55000 = 2500 h 22 yards = height ********************************************* Jenn Cody Mt. St. Joseph Academy Grade 10 First, I figured out the volume of the of the area the man plowed using the following formula: V=l*w*h The length, width, and height of the area was given. l= 1 mile w= 50 yardsh= 30 inches Since the measurements are in different units, I changed them into feet by doing unit conversions and got the following: 1 mile=5280ft50yd=150ft30in=2.5ft V= 5280ft*150ft*2.5ft V= 1980000ft^3 Then, I divided the total volume by 4 the get the volume of each pyramid. V= 495000 ft^3 I found the height of each pyramid by using the following equation for the volume of a pyramid: V=Bh/3 ( B=area of base)B=50yd*50yd 495000ft^3 = 22500ft^2 * h / 3B=150ft*150ft (Area of base 495000ft^3 = 7500ft^2 * hB=22500ft^2 of pyramid) 66ft = h 22yd = h ********************************************* Lindsay Pio Grade 9 Mount Saint Joseph Academy To find the answer for this week's problem of the week, I first drew a diagram of what the runway would look like. I then labeled all of the measurements. To find the area of the runway I multiplied the height, 30 inches or 2.5 feet, the length, 1 mile or 5280 feet, and the width, 50 yards or 150 feet. All of that multiplied together is 1,980,000 feet. Then I divided that answer by four since he made four pyramids. I then got 495,000 feet, which is how much snow is in each of the four pyramids. Then I looked up the formula for finding the area of a pyramid - V= 1/3 BxH. I got the base as 22,500 ft. by multiplying 150 by 150 (50 yards) because you said the bases of the pyramid were 50 yards by 50 yards. So, my equations for solving this problem are: V=BxH, 495,000= 1/3 (22,500)H, and 495,000= 7,500 H, and 66 ft.= Height. The height of one of the pyramid is 66 feet. ********************************************* Susan McGowan Sophmore-Mt. St. Joseph Academy When I was given this problem I decided to first change all of the measurements into feet. Through this I got: 50yds.- 150ft 1 mile - 5280ft. 30 ins. - 2.5ft. I then found the volume of the snow by multiplying the measurements together. I got 1,980,000 cubic feet. I then divided this by four, because there were four pyramids. The answer was 495,000 cubic feet. I then used the formula for finding the volume of a pyramid. V=Bh/3 which equaled--495,000 ft3=22500 ft2 h/3. (22500 is the area of the base). Through cross multiplication I came up with the equation 1,485,000 ft3 = 22500 ft2 h. After dividing each side by 22500 ft2, I got the equation 66ft=h. And so, the height of each 66ft. or 22yds. ********************************************* Lauren Wall & Lindsay Parsons Mount Saint Joseph Aceademy Grade 9 We solved this problem by performing a series of equations and using various formulas of geometry. First we converted each of the measures to feet; then, we multiplied these numbers together to find the volume of the snow to be plowed. The operations were like this: 150ft.*5280 ft.*2.5ft.=1,980,000 cubic feet. We then divided this figure by 4 for the 4 square pyramids given to find the volume of snow for each, and we came up with 495,000 cubic feet. We then set up an equation using the formula for the volume of a square pyramid. Since height was the unknown, we put in the Base (area of the square base) and the volume. The equation looks like this: 1/3Bh = V. 1/3 (150*150)h = 495000. 7500 h = 495000. The measurements of 150ft. come from the 50 yard figure given. When we performed the operations we found that the unknown height of the square pyramids was 66ft or 22 yards. ********************************************* Jackie Benn and Shannon Firth Mount St. Joseph Academy Problem of the Week 1/8-1/12 The height of the pyramids is 22 yards. First we took our given, we knew that each base of the pyramids was 50 yards (pyramids have four bases) and that the area this artistic dude was plowing was 50 yards wide, one mile long, and 30 inches thick. First we converted everything into inches and found the volume to be 3421440000 inches cubed of the area plowed. We divided the area plowed into four equal parts and got 855360000 inches cubed. This is the volume of each individual pyramid. Then we multiplied 50 times 50 and got 2500 yards squared (or 32400 in). Knowing that the formula for finding the height of a pyramid is h=3v/b, we applied our numbers to the formula. Now, our problem looks like this: height= 855360000 inches cubed x 3/ 3240000 After doing the math, we calculated that the height of each individual pyramid must be 792 inches high or 22 yards high. ********************************************* Michele Weiss & Jackie Mattera Mount Saint Joseph Academy Grade 9 To figure out how tall each snow pyramid was, first, I converted all of the measurements into inches. (As you can probably guess, my numbers were very big.) Then, I found the volume of the area he had to plow. I divided that volume by four so I could get the volume of each of the four pyramids he made. Since I know that each edge of each pyramid is 50 yards, I can figure the area of the base. I then converted that answer into inches. Now that I have the area of the base of one of the pyramids and the volume of one of the pyramids, I can figure out the height by solving for the unknown variable in the formula for the volume of a pyramid. That formula is: V=1/3 Bh The height that I got was 792 inches or 22 yards. ********************************************* Claire Bonner, Christina Niescier Mount St. Joseph's Academy Grade 10 P.O.W 1/8-12/96 To figure out the height of the snow pyramids, we first converted the measurements to feet. We first calculated the total volume of snow to see how much we were dealing with. The total amount of snow was 1,980,000 cubed feet. Since there were four pyramids, we divided the total volume by four and got 495,000 cubed feet. We then looked into our geometry book to see how we could find the height from this information. I found this formula, Volume of Pyramid = Area of Base times Height. We knew the volume and the are of the base, 22,500 sq. ft., and we were looking for the height. This equation was just right. We moved the equation around to fit our purposes and plugged in the numbers. The height of each of the four snow sqare pyramids was 22 yards. ********************************************* All your units are screwy. Nonetheless, using the formula V=1/3*b*h and a whale of a lot of conversion factors, I find that the volume of each pyramid is 220,000 cubic yards, and that the height (in the one English unit you didn't use) is 66 feet. Benjamin Warfield, Grade 12 Garfield High School, Seattle ********************************************* From: Jon Tan Grade: School: dlsu Answer: volume of snow = volume of 4 pyramids volume of 4 pyramids = (4*b*h)/3 = (4*2500*h)/3 volume of snow = b*w*h = 50 yards * 1 mile * 30" = (125*1760)yards/3 by equating volume of snow = volume of 4 pyramids we get the height of each pyramid equal to 22 yards ********************************************* From: Brian Gordon Grade: 1992 School: Dartmouth Answer: Hi Annie, here's this week's answer: First, the volume of the snow is 5280 feet x 150 feet x 2.5 feet = 1,980,000 cubic feet of snow. Next, this has to be equal to four times the area of each pyramid. Each pyramid has volume 1/3 x 150 feet x 150 feet x height. So the equation is: 4 * 1/3 * 150 * 150 * h = 1,980,000 Divide by everything to get h = 66 feet, or 22 yards. --bri p.s. we only got about 18-20 inches here in Middletown, CT. ********************************************* From: Ken Duisenberg Grade: Post-Master's School: California State University, Chico Answer: The pyramids are each 22 yards high. The area of a pyramid, with base area A and height h, is: Ah/3. The base area of each of the four pyramids is 50*50 sq.yds. The total volume of the pyramids is thus 50*50*4h/3 cu.yds. The total volume of snow (assuming it keeps the same volume upon being plowed - quite unlikely, I'd think) is (1mi.=1760yd.): 50*1760*(5/6) cu.yds. Setting these equal and solving for h, finds h=22yds.
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