Practical Geometry

• Coordinate Systems, Longitude, Latitude [Harris, 04/19/1997]
  Can you explain pitch, roll, and yaw to me? Are there other systems for measuring an object's position in space?

• Frustum of a Cone [Blackburn, 12/09/1996]
  If you cut a cone and then lay it out on a flat surface, what will be the inside and outside sizes of this flattened-out cone?

• Jobs That Use Geometry [Keesha, 12/18/2001]
  I would like to learn how geometry is used in real life. What jobs involve geometry?

• Three Tapers and a Length [Larry, 8/25/1995]
  I have three tapers (or angles) that intersect with each other. Theoretically, if I were given the total length from 0 to Y and the total height 0 to X and of course the three angles, is it possible to calculate each angles length and height?

• Daylight Hours and Latitude [Chen, 1/9/1995]
  How does the number of daylight hours on a given day of the year depend on latitude?

• Volume of a Pond [Burnett, 2/1/1995]
  I need to have a large pond cleaned at my place of employment. The pond is completely filled with waste material and I would like to know how many cubic yards are in the pond to remove.

• Using Geometry to Make a Roof [Robertson, 8/30/1995]
  I'm not a student but a wood worker with a question on solid geometry. I want to know how to calculate the angle on the sides of triangles in order to form a cone shaped (not round but angular) roof.

• Building a Skateboard Ramp [Inowick, 9/19/1995]
  I'm trying to build a skateboard ramp, pyramid with flat top, height one foot, angle of ascent thirty degrees, other angles ninety degrees and sixty degrees. If the height is one foot, what are the measurements of the other two sides of the triangle ( the base and the slope)?

• Making a Pool Tarp [Reynolds, 9/27/1995]
  I'm trying to construct a pool frame out of pvc that will be placed over a pool. We already have the pool tarp, but we need to build something that will shed water so it has to have a slope. PVC only comes in 90 degree and 45 degree angles and straight sections. How do I figure out the maximum height the frame can stick straight up in the air to utilize the tarp?

• The Angles of a Roof [Homan, 11/20/1995]
  I am trying to build a model house but am having trouble with laying out the roof. The main part of the house has a peaked roof (an "A" frame house); the angle formed when the roof meets the ground is 60 degrees. There is an addition onto the A-frame with a 30 degree angle formed to the walls. What angle should the addition's roof be cut at so it meets the A-frame roof?

• How Many Liters of Water Does a Pool Hold? [Collingham, 12/4/1995]
  A pool's surface forms a rectangle 25 meters long by 15 meters wide. The pool is 2 meters deep at the shallow end and the depth increases at the constant rate to four meters at the other end. How many liters of water will the pool hold?

• Finding the Circumference of a Circle Using Its Shadow [Oldenberg, 1/26/1996]
  I am attempting to find the circumference of a large sphere that is hanging 25 feet in the air.

• Finding the Radius of a Pipe [Phillips, 1/28/1996]
  A pipe has become bent and is no longer round. In order for me to correct the problem, I must build a brace to go around the pipe and true it up. However, until I can determine the radius of the pipe, a brace cannot be built.

• Cutting Cake with Geometry [Mittledorf, 2/4/1996]
  A cake is square when viewed from the top. Height is unspecified. It is iced on top and the four vertical sides. How can the cake be divided in 5 pieces such that each piece has the same amount of cake and the same amount of icing? How can you minimize the number of cuts you have to make in the cake and still meet this target? Alternatively, how can you minimize the total length of the cuts you make in the cake?

• Filling a Garden with Topsoil [Blind, 2/5/1996]
  I have a garden that is 10' x 10' (100 square feet). I want to add 6" of topsoil to my garden. Topsoil is sold by the cubic yard. How many cubic yards of topsoil will I need for my project?

• Finding the Volume of a Horizontal Tank [Silva, 2/13/1996]
  What is the formula for finding the volume of a horizontal cylinder?

• Spiral Baffle in a Cylinder [Styms4, 6/24/1996]
  We have a cylinder, 48 inches in diameter, to put a spiral baffle inside... What would the radius be?

• The Law of Margins [Nilan, 9/2/1996]
  How do I figure out the margins of my mat using the Golden Ratio?

• Rectangle Needed To Make Cone [Thompson, 9/5/1996]
  I want to make a lampshade by rolling a piece of paper into a non- closed cone shape...

• Cutting Carpet [Andriano, 9/9/1996]
  Two pieces of carpet are to be used to cover a floor. You are allowed to make just one cut in one of the two pieces...

• Side Length of Octagon Inscribed in Square [rtynan, 9/11/1996]
  I have a piece of square plywood (48" on a side) and I would like to cut an octagon out of the middle. What is the side length of the octagon?

• Fitting a Picture to a Frame [Stoll, 11/14/1996]
  I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

• Optimization [Sanec, 11/26/1996]
  To make a funnel, we take a circular piece of metal, cut out a sector, and connect the two radial edges together to make an open cone. What should the angle of the sector be to maximize the volume of the cone?

• Area of an Unusual Hexagon [Fletcher, 12/05/1996]
  Find the area of a hexagon made from a triangle with squares appended to each of its sides and three more triangles each consisting of one unknown side and two sides which are shared with two of the squares.

• Finding the Center of a Circle [Heikke, 12/26/1996]
  Given a circle of radius R with center point unknown, a line with equation Y = mx+b and a line at Y = -.08, find the x,y coordinates of the points of tangency where the two lines intersect the circle.

• Hole in a Sphere [Klein, 12/30/1996]
  When you bore a 6 inch cylindrical hole through the center of a sphere, what is the volume of the remaining solid?

• Earth's Curvature [Choksi, 01/27/1997]
  How do you figure out the degree of curvature of the earth's surface?

• Roof Rafters [Badalamenti, 02/03/1997]
  What is the formula that gives the length of a roof rafter if only the pitch of the roof is known?

• Maximizing Window Area [Pierre, 02/24/1997]
  Maximize the area of a Norman window (rectangular with a semicircle on top) while minimizing the length of the perimeter.

• Civil Engineering and Math [ehsmc, 02/25/1997]
  What forms of math or physics do civil engineers commonly use?

• Triangular Garden [Ferguson, 03/18/1997]
  Find the length of a fence that runs from the right angle to the hypotenuse and separates the garden into two parts of equal perimeter.

• Perimeter of Octagon [Rodano, 04/02/1997]
  What is the perimeter of a an octagonal garden with a diameter of six feet?

• Pyramid Construction [Mohr, 05/24/1997]
  How do you figure out the angles necessary to construct a pyramid out of plywood?

• Making Labels for Cones [Krone, 06/26/1997]
  How do you make a label that will fit on a yogurt container without puckering?

• Painting a Column [Ryan, 07/13/1997]
  If I have a column 9.5' long and 8'' in diameter, how do I figure out how much paint I need to cover the outside area?

• Find the Diagonal of a Rectangle [Henderson, 07/26/1997]
  We use a tape measure to square different things on the job site by measuring opposite corners...

• A-frame for Swing [Ribblett, 07/26/1997]
  I am trying to build a stand for a swing. The ends are A-frames out of 4 by 4's... what is the angle of the miter cut?

• Miter for a Pyramid [Champion, 07/31/1997]
  I want to construct a 4-sided pyramid out of glass for a garden fountain. I need to know the degree of miter to put on the edges of the uprights of the triangles...

• Lengths of a Sixteen-sided Circle [Richards, 08/05/1997]
  I would like to make a sixteen-sided window for the second floor hallway of my twin girls' playhouse.

• Wood Flooring [Taylor, 08/09/1997]
  Estimating the number of lineal feet in 1 sq. ft., making wood flooring 3.25 inches wide, producing 5,000 sq. ft. per day.

• Tape Measure Markings [Greg, 8/11/1997]
  What is the small diamond on all tape measures that occurs every 19.2 inches for?

• Volume of Water Passing through a Pipe [Veronica, 08/12/1997]
  How many gallons of water per minute can a 12" cylinder pipe handle?

• Length of a Roll of Carpet [Massey, 08/21/1997]
  How can you determine the length of a roll of carpet without uncoiling it?

• Bricks to Cover a Steeple [Rector, 08/23/1997]
  How many 6"x12" bricks would it take to cover an octagonal steeple with a diameter of 130 ft. and a height of 370 ft?

• Pipe Needed for Natural Gas Line [Santana, 09/03/1997]
  Two houses are 130 metres apart at distances of 55 and 105 metres...

• Depth of a Tank [Rossman, 09/04/1997]
  A tank 100' long and 10' wide holds 15,000 cu. ft. of water...

• Volume of Dirt [Budzynski, 09/29/1997]
  You have a mound of dirt that is 2 meters high with a bottom radius of 1 meter...

• Foil Wrapped Around a Spindle [Brown, 12/17/1997]
  I have a problem in an engineering work environment. I need to know the length of foil (L) needed to generate the external diameter...

• Areas of House Lots [Redfearn, 02/18/1998]
  We have to determine sanitary sewer assessments of properties based on the square feet of their lots. Many lots are 4-sided but do not have any parallel lines...

• Deriving the Volume of a Frustum [Taylor, 05/06/1998]
  Can you derive the formula for the volume of a frustum of a cone?

• Parabolic Equation of an Arch [Child, 05/25/1998]
  Finding the equation of the parabola in the McDonald's golden arches.

• Radius of an Arch [Bullard, 05/25/1998]
  Is there a formula to calculate the radius of a circle given the chord length and the distance from the centre of the chord to the circle?

• Ellipse Geometry [Crosbie, 08/09/1998]
  I wish to draw a line departing at a given angle from the long axis of an ellipse and bisecting the perimeter of the ellipse at right angles to the tangent at that point...

• Azimuth Angle [Harrington, 09/08/1998]
  Can you give me the formula for the azimuth angle and explain some of the terminology?

• Latitude and Longitude and Daylight Hours [Fiva, 09/21/1998]
  Is there a formula for calculating the number of hours of daylight, given the latitude and longditude of a point on the globe?

• Rhumb Lines and Great Circle Routes [Leeds, 09/24/1998]
  Can you explain great circles and rhumb lines and how they relate to shortest distances in geometry?

• Ratios and Geometry [Blackwood, 10/29/1998]
  An airplane flying at 33,000 feet has a visibility of 100 miles. What percent of the total land area to the horizon is visible?

• Linear and Board Feet [Sam, 01/04/1999]
  Can you explain the terms linear foot and board foot as they are used in the lumber industry?

• Horizontal Gas Tank Content Formula [Austrino, 01/17/1999]
  Can you help me find a formula to measure the volume of gas left in a horizontal gas tank given the height of the gas and the dimensions of the tank?

• Miter Angle of a Pipe [Bruce, 02/10/1999]
  Find the miter angle of a pipe of certain shape.

• Accurate Drawing of an Ellipse [Patrick, 02/14/1999]
  Draw an ellipse accurately using simple tools.

• Volume of Soil [Amy, 02/16/1999]
  How many cubic feet of soil will be needed to fill a 2x6x4x4' by 8" trapezoidal garden bed?

• Liquid in an Elliptical Tank [Tom, 02/28/1999]
  Given any height of liquid, say 3 ft., how can I calculate the volume?

• How Much Carpet is Left? [Gillette, 03/27/1999]
  We use rolled carpet in our business and would like to know how much is left on a roll given the remaining diameter...

• Filling Cylindrical Holes [Raue, 05/18/1999]
  What volume of cement, in cubic yards, will fill 42 holes that have a 9" diameter and are 4' deep?

• Determining Cone's Original Dimensions from a Slice [Branson , 05/18/1999]
  Given the inside and outside arc lengths and the thickness of a truncated cone, find the inner and outer radii and the angle.

• Will the Tree Hit the House? [Madison, 05/18/1999]
  A tree is leaning at 70 degrees, our house is 66 1/2 feet away, and the angle from our house to the top of the tree is 40 degrees...

• Constructing a Pyramid [Daniel, 05/28/1999]
  How can I calculate the sides and angles needed to construct a pyramid with an 8-foot-square base and a height of 6 feet?

• Scanning for Mountains [Kwok, 06/02/1999]
  I am standing on a hill scanning the horizon to see a mountain. How high must the mountain be for high-tech optical equipment to be any use?

• A Pyramid of Layered Marbles [Chris, 06/02/1999]
  How can I find the number of layers, the number of marbles, and the size of a container containing a pyramid of layered marbles?

• Surveyor's Formula [Pagani, 06/05/1999]
  Can you give me a method to calculate the area of an irregular polygon given all the coordinates of the points?

• Ratios, Geometry, Trigonometry [Cathy, 06/10/1999]
  A homeschool teacher asks for help with triangles, flagpoles, and circles.

• Maximizing the Volume of a Box [Sherrillo, 06/27/1999]
  I have a piece of glass that is 14" by 72". What dimensions would I need to make a glass cage with maximum volume?

• Tiling a Floor [Melissa, 06/30/1999]
  How many square yards is a 12ft. by 15ft. room? How many 8" x 8" tiles would you need for a 30 sq. ft. room?

• Maximizing Volume of a Box [Baker, 07/08/1999]
  Why are cereal boxes the size they are? Is it just to maximize volume?

• A 'Pyramiddle' Tent Problem [Hufnagel, 07/12/1999]
  Figure out an equation that yields d when values for h and r are inserted.

• Pixels in a Triangle [Cambazoglu, 08/02/1999]
  How can I find the number of pixels inside a triangle?

• Angle Between Two Sides of a Pyramid [Lukens, 10/29/1999]
  How can I compute the angle formed by two sides of a frustrum of a pyramid?

• Volume of Liquid in a Cylindrical Tank [Mustapha, 05/08/2000]
  How can I calculate volume of liquid in a cylinder that's not full and lying horizontally?

• Teaching about Bearings [Widdicombe, 06/08/2000]
  What are bearings? Do you have any ideas on how I can present bearings to my math class in an interesting fashion?

• Tanker Bearings [Crane, 06/11/2000]
  From ship A, the bearing of an oil tanker is 300 degrees; from ship B, 1000 m due west of A, the bearing of the tanker is 060 degrees. Is the oil tanker the same distance from A as from B?

• Finding the Radial Separation of a CD Track Spiral [Giles, 10/04/2000]
  On audio CDs a track of pits spirals outward from a radius of 25 mm to a radius of 58 mm. How can I calculate the radial separation of the pits?

• Flattening the Frustum of a Cone [Scholl, 10/15/2000]
  We are building a desk the front of which forms a section of a cone. We know the radius and chord length at the top and the floor. How do we generate a flat layout of this section?

• Applications of Parabolas [Lau, 10/24/2000]
  How are parabolas used in real life?

• Compound Angles [Mangwiro, 01/14/2001]
  A rail does not go into a post horizontally, but has a rise angle of 30 degrees and a side angle of 39 degrees. The hole to be routed needs to be a parallelogram instead of a square...

• Finding the Axes of an Ellipse from a Known Cone [Mion, 01/26/2001]
  I'm trying to solve a specific situation regarding lighting when viewed as an oblique circular cone...

• Building a Wooden Square-Based Pyramid [Hosler, 01/26/2001]
  I want to build a wooden pyramid with a square base 8"by 8".

• Longitude-Latitude Product and Distance [Abdullahi, 02/14/2001]
  Is the difference between the product of the longitude and latitude of one point and that of another point related to the distance between them?

• Pattern for Lampshade [Loraine, 02/17/2001]
  I would like to know the formula for computing the surface area of a lamp shade so that I can make a pattern from it.

• A Practical Use for the Orthocenter [Hodel, 03/07/2001]
  Does the orthocenter of a triangle have any practical uses?

• Fabric Left on a Roll [Rob, 03/15/2001]
  I am going to write a program for my TI-83+ to calculate how many feet of material are left on a roll.

• Parabolas in Everyday Life [Ledesma, 05/18/2001]
  What types of things have been made using parabola shapes?

• Sizing a Connector [Tom, 06/01/2001]
  I have to come up with a specific diameter for anywhere from 2 to 91 diameters that are bunched together. The application is round wires.

• Calculating the Angle of a Plank [Nick, 08/22/2001]
  Are there any equations that could be used to solve for a plank of known width?

• Segment of an Ellipse [Martin, 09/06/2001]
  We often use horizontal oval tanks for storing drinking water and fuel, and we would like to be able to calculate the contents.

• Carpet Problem [Nathan, 10/15/2001]
  You have to carpet a 9x12 room, but when you go the store they only have a 10x10 carpet and a 1x8 piece of carpet...

• Carpet and Room Areas [Matt, 10/26/2001]
  A man buys a roll of carpet 9 ft. wide by 12 ft. long to fit a 10ft. by 10 ft. room. When the roll of carpet is unrolled, a hole is discovered in the middle of the carpet...

• Building a Cone [Gary, 10/28/2001]
  I am trying to find a formula for building a cone for a chimney flashing. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2".

• Kitchen Tabletop [Russell, 11/21/2001]
  I need to determine the correct pivot point...

• Longest Ladder [Michelle, 11/30/2001]
  Two hallways, one 8 ft. wide and other 4 ft. wide, meet to form a right angle. What is the longest ladder that can go around the corner where the hallways meet?

• Building a Manger [Anne, 12/03/2001]
  Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

• Calculating the Length of String on a Reel [Larry, 12/07/2001]
  Is there a formula for calculating the length of wire that can go on a reel (spindel) where the reels may have different diameters, hub diameters, and widths, and the wires may have different diameters?

• Oil Can Dimensions [Shannon, 12/11/2001]
  What are the dimensions of an oil can with a one-liter capacity that uses the least amount of tin?

• Volume of Partially Full Cylinder on its Side [Charlie, 12/31/2001]
  I am in charge of ordering fuel for our company, and the way the owner calculates the volume is via a grossly simplified percent full guesstimation...

• Woodworking Curve [Tony, 02/06/2002]
  I am making a cabinet and I want to put a curve on the front of the shelves. The "chord" of the circle would be 15" and a perpendicular line from the center point of the chord to the circumference of the circle is 1".

• Frustum of a Pyramid with a Rectangular Base [Brad, 02/20/2002]
  I am an engineer with a water treatment agency and need to figure the amount of water per foot of elevation in our reservoirs...

• Swimming Pool Volume [David, 02/28/2002]
  What formula would I use to calculate the volume in gallons of a swimming pool 135' x 70' with different depths of 3', 5', 8' and 11'?

• Finding Miles Per Hour [Joshua, 03/06/2002]
  If a wheel is making 64.2 revolutions per minute, how many miles per hour is it going?