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Browse High School Practical Geometry

Stars indicate particularly interesting answers or good places to begin browsing.



Cutting a Circle out of a Square [2/14/1996]
What is the area (to the nearest square centimeter) of the largest circle that can be cut from a square piece of sheet metal 73cm. on each side? Explain how you determined this.

Cutting Cake with Geometry [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?

Cutting Carpet [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...

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

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

Designing and Building a Cone Frustum [03/24/2004]
I need help making making a pattern for a frustum shape to protect a large piece of equipment. How can I find the distance between the top and bottom arcs in a straight line?

Determining an Angle From Side Views [07/24/2002]
In the end elevation of a drawing, a rod rises from point A at 32 degrees. In the side elevation, the same rod is seen rising from point A at 48 degrees. How do I work out at what angle to cut the end of the rod?

Determining Cone's Original Dimensions from a Slice [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.

Determining Length of Material Remaining on a Roll [11/24/2003]
Is there a mathematical formula to determine the length of material on a roll, given the outside diameter of the core, the outside diameter of the whole roll, and the thickness of the material (determined by a micrometer)?

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

Ellipse Geometry [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...

Elliptical Orbits in the Solar System [05/22/2005]
I want to have my students draw a scale model of the solar system that shows the orbits of the planets. Assuming I have the apogee and perigee of each planet's orbit about the sun, they need to construct 9 ellipses with some degree of accuracy. What's the best way to go about this?

Equation for an Arch [09/09/1997]
I am trying to draw an arch that will go in the ceiling of a building. The arch will be at a maximum height of 28 inches...

Fabric Left on a Roll [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.

Filling a Garden with Topsoil [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?

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

Finding a Plane Shape for a Truncated Cone [05/10/2000]
What is the best way to cut a flat two-dimensional piece of sheet metal into a three-dimensional truncated cone?

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

Finding the Angle of Solar Collectors on a Sloped Roof [08/30/2008]
I have solar collectors on my roof. They are mounted so that the base of each panel runs up the slope of the roof, and the panels themselves are mounted at an angle. I'd like to know how to determine the various angles created by this situation.

Finding the Area of an Irregular Shape [01/03/2007]
I need the area of a parcel of land with 5 sides. I know the lengths of the sides and the angles at the corners, but am not sure how to calculate the area.

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

Finding the Center of a Disk [12/13/2002]
I need to find the center of a solid disk to bore a hole.

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

Finding the Length of Carpet Left on a Roll [09/25/2008]
If I can see the end of a roll of carpet I can figure out the approximate square yardage by taking the inside circumference, the outside circumference and the number of total layers left, then calculating each layer. Is there a formula I can apply to calculate the result directly?

Finding the Radial Separation of a CD Track Spiral [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?

Finding the Radius of a Pipe [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.

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

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

Fitting a Picture to a Frame [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?

Flattening the Frustum of a Cone [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?

Foil Wrapped Around a Spindle [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...

Formula for Laying Out an Arc [09/27/2002]
I need a formula for laying out an arc using a known radius and distance from the chord to the arc at 90 degrees.

Gas in a Cylindrical Tank with Hemispheric Caps [02/09/2010]
Doctor Jeremiah uses calculus to calculate how much gas a large pill- shaped tank holds.

Geometry Unit on Quilting [07/16/1997]
Do you have any information/units/lessons/curriculum ideas on quilting in mathematics?

Given Octagon Diameter, Find Side Length [04/09/2003]
If you have the diameter of an octagon, what formula gives you the length of the sides?

Hole in a Sphere [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?

Horizontal Gas Tank Content Formula [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?

How Many Liters of Water Does a Pool Hold? [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?

How Much Carpet is Left? [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...

How Much Material on a Spool? [05/02/2007]
A reel of flat blade has an outer diameter of 1016 mm and an inner diameter of 508 mm. The blade thickness is 20 mm. Could you tell me the length of the blade and show me the formula for working it out?

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