Ask Dr. Math

High School Archive

Browse High School Higher-Dimensional Geometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Do cones or cylinders have edges?
    Latitude and longitude.
    MaximizIng the volume of a cylinder.

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Finding the Circumcenter of a Sphere [09/24/2003]

How can I find the circumcenter of a sphere given 3 points on the sphere, along with the radius?

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 Radius of a Sphere [10/28/1996]

Can you find the radius of a sphere if you don't know the volume or surface area?

Finding the Volume of a Horizontal Tank [2/13/1996]

What is the formula for finding the volume of a horizontal cylinder?

Finding Where Planets are Rising/Setting [03/12/2002]

Find a formula that calculates where (in longitude and latitude) the different celestial bodies are on the horizon, either setting or rising.

Find the Cities [06/19/2001]

Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find every city within 10 miles of a straight line between them.

Five Equal Pieces of a Square Cake [05/22/2001]

Ravina wants to cut a square cake using straight vertical cuts to make five pieces of equal volume. If she makes the first cut from the cake's center to the top left corner, where must she make the other cuts if they all start from the cake's center?

Flattened Cone [08/30/1998]

Drawing a shape you could cut out and roll up to form a cone whose cross-section you are given.

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?

Floating Copper Ball [02/26/2002]

Find the wall thickness of a hollow copper ball (sphere) with an outside radius of 50.0 cm that "just floats" in water.

Formation of a Cone [03/16/2003]

Why is a cone formed when a sector is removed from a circle and the edges of the remaining segment joined?

Formula for Radial Latitudes and Longitudes [10/15/2002]

I want to make a radius search tool that returns all places based on latitude/longitude within a certain radius of a given place.

Formula for the Curvative of a Curve [10/10/2002]

Is there a formula or theorem I can use to convince someone who believes a wall has only side that there is another side to it?

Formula for the Surface of a Cylinder [7/2/1996]

What is the general formula for the surface of a cylinder?

Formulas for N-Dimensional Spheres [10/26/2000]

What is the next term in the sequence pi*r^2, (4/3)pi*r^3, ...? Would it be the formula for the volume of a 4-dimensional sphere?

Frustum of a Cone [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?

Frustum of a Pyramid with a Rectangular Base [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...

GPS Formula [11/27/2002]

How can I calculate the position from 3 points (or more) in latitude longitude format?

Great Circle Parametric Equation [05/25/1998]

How can you calculate specific points of a great circle on a sphere? Can you help me find the parametric equation?

Height of a Dome [08/06/2002]

On a perfectly circular, small, flat island, a glass dome covers the island, forming a perfect hemisphere. If the canopy is 10 feet tall at the center of the island, how far from the center can 6-foot-tall Omar walk upright?

Helpful Ways to Remember Cylinder and Prism Formulas [03/28/2005]

I was wondering if you could tell me an easy way to memorize formulas like volume, surface area, and lateral area for cylinders and prisms?

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 Dimensions Are There? [03/29/2001]

How do we know how many dimensions there are? What is the significance of drawing 4D hypercubes? If I were in a 2D world, how would I be able to represent 3D objects?

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 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?

Hypercube [10/13/2001]

Have there been any recent developments in studying the fourth dimension?

Hyperspace and the 4th Dimension [9/20/1995]

May we have a general definition of hyperspace?

Information About Topology [11/12/1996]

Where can I learn more about topology?

Intersecting Lines Coplanar? [08/23/2002]

Do two intersecting lines have to be coplanar?

Intersection of Three Spheres [06/05/2003]

How do you find the intersection of three spheres?

Intersection of Two Spheres [10/13/2003]

How can I find the equation of the circle that results from intersecting two spheres?

Is a Curved Surface a Face? [03/19/2008]

Is a curved surface a face or not? Like in a cylinder, is the curved surface considered a face?

Is Geometry a Language? [01/28/2002]

I have to write an essay to defend or criticize the statement, "Geometry is a Language."

Isoperimetric Quotient [03/11/2002]

Is there an equation for the ratio of surface area to volume?

Jobs That Use Geometry [12/18/2001]

I would like to learn how geometry is used in real life. What jobs involve geometry?

KaleidoTile [11/15/1995]

I would appreciate it if you would tell me a bit about KaleidoTile.

Klein Bottles and Mobius Strips [08/09/1999]

How is the Klein bottle related to the Mobius Strip? Why can't I construct a Klein bottle in 3-dimensional space without intersection?

Knot Theory [10/24/1996]

What does Knot Theory actually describe and mean, what does it state about knots, and what is its usefulness in real life?

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