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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.

Volume and Surface Area of a Cone Frustum [08/30/1999]
Can you show me how the formula for the volume and total surface area of the frustum of a right circular cone is derived?

Volume by Inch of a Cone-Shaped Tank [03/03/2003]
I have a chemical tank that has a cone bottom and I need to know the volume of each inch of the cone.

Volume of a Cone [02/08/2002]
I have observed that a cone consists of a right triangle and a circle base, and I have came up with another method of calculating the volume of a cone...

Volume of a Cone [5/9/1996]
How much coffee can a tapered coffee pot hold?

Volume of a Cone [02/19/1999]
Prove that the volume of a cone is one-third that of a cylinder with the same height and radius.

Volume of a Cone [01/29/2001]
I know HOW to find the volume of a cone (1/3area of base times height divided by three) but my teacher wants to know WHY...

Volume of a Cone or Pyramid [03/30/1998]
Proofs that the volume of a cone or pyramid is (1/3)b*h.

Volume of a Conical Wedge [03/04/2002]
Two porters agree to drink off a quart of strong beer between them, at two pulls, or a draught each...

Volume of a Cylinder [09/05/1997]
How do you calculate the volume of a cylinder laid on its major axis if you know the heights of the top and bottom of the section?

Volume of a Cylinder [7/30/1996]
What is the volume of the storage tank with a diameter 6m, height 5m?

Volume of a Cylindrical Tank [2/3/1995]
I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if they were standing on end...

Volume of a Dome [03/09/1999]
Is there a formula for the volume of a dome?

Volume of a Frustum Cone [03/20/2001]
Given a frustum cone with a bottom radius of 4", a top radius of 2", and a vertical height of 12", find the interior heights if the volume is divided into equal thirds.

Volume of a Frustum-Like Structure [05/12/2000]
How can I calculate the volume of a frustum-like structure with a rectangular base and rectangular top whose dimensions are: top: 73x37, bottom: 46x10.5, angle: 18 degrees, and height: 4.6?

Volume of a Hemisphere Using Cavalieri's Theorem [09/09/99]
How can I derive the formula v = (2/3)pi R^3 for the volume of a hemisphere of radius R using Cavalieri's theorem?

Volume of a Horizontal Cylindrical Tank with Elliptic Heads [11/15/2003]
I need an equation that will relate the height of liquid to the volume of liquid partially filling a horizontal cylindrical tank with elliptic heads.

Volume of an Elliptical Cone [10/15/1998]
Can you help me on find the volume for an elliptical cone by using a triple integration?

Volume of an Elliptical Frustum [12/01/1999]
What is the volume of an elliptical frustum?

Volume of a Pond [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.

Volume of a Prismatoid [10/21/2008]
How can I calculate the volume of a pyramid for which the bottom end is rectangular and the top end is circular?

Volume of a Pyramid [5/20/1996]
All six edges of a triangular pyramid are 4 inches long. Find the volume of the pyramid.

Volume of a Pyramid [09/01/1998]
How can you prove algebraically and geometrically that the volume of a pyramid is (1/3)b*h?

Volume of a Rectangular Solid [4/4/1996]
How do you calculate the lateral area, total area, and volume of a rectangular solid with the following dimensions...

Volume of a Right Circular Cone [10/07/2001]
Using calculus, derive the formula for the volume of a right circular cone with a radius of r and height h.

Volume of a Rounded Horizontal Tank [03/26/2004]
What is the formula for finding the volume of a rounded horizontal tank (capsule-shaped) based on the height of the liquid in the tank?

Volume of a Solid [10/02/1997]
The base of a solid is the region inside the circle x^2 + y^2 = 4...

Volume of a Sphere [04/21/1998]
Can you help me derive and prove the formula for the volume of a sphere?

Volume of a Sphere [05/28/1999]
Why is the volume of the sphere V = (4 Pi/3)r^3?

Volume of a Sphere [05/19/2002]
Where does the (4/3) come from in the formula for the volume of a sphere?

Volume of a Spherical Cap [12/06/2000]
How can you derive the formula for the volume of a spherical cap without using calculus?

Volume of a Trapezoidal Solid [11/15/2000]
How can I find the volume of a figure formed by two aligned noncongruent rectangles connected by planes?

Volume of a Triangular Tank [8/5/1996]
What's the volume of a triangular tank 3'4"x3'4"x5' and 22" in height?

Volume of a Truncated Cylinder [05/07/2000]
How can I find the volume of a cylinder that has had part of its top and bottom removed?

Volume of a Tube Converted to Gallons [08/01/1997]
I have a length of round pipe that is 4" in diameter and 10 feet long. How many gallons of water will it hold if filled and sealed at both ends?

Volume of Cube, Tent [7/9/1996]
How do I calculate the volume of a cube and a tent... and the capacity of a cylinder and a tent?

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

Volume of ellipsoid [05/22/1997]
I have forgotten how to calculate the volume of ellipse.

Volume of Ellipsoidal Cap [04/11/2001]
I am doing research on cancer and need a way to properly determine the volume of tumors in lab animals.

Volume of Inscribed Cylinder [08/14/1997]
A cylinder of height h is inscribed in a sphere of radius q. Find an expression for the volume of the cylinder.

Volume of Intersecting Pipes [10/27/2000]
How can you calculate the volume of the intersection of two perpendicular pipes of the same radius?

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