Ask Dr. Math
High School Archive
Dr. Math Home ||
Middle School ||
High School ||
Dr. Math FAQ
See also the
Dr. Math FAQ:
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 Pi [11/10/1997]
How do you find the volume of a cylinder that is 7.5mm high and has a
diameter of 4mm?
- 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
- 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
- Volume of an Elliptical Cone [10/15/1998]
Can you help me on find the volume for an elliptical cone by using a
- 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
- Volume of a Spherical Cap [12/06/2000]
How can you derive the formula for the volume of a spherical cap without
- 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
- 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
- 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.
Search the Dr. Math Library:
© 1994- The Math Forum at NCTM. All rights reserved.
Home || The Math Library || Quick Reference || Search || Help