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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Calculating How Much Paper Is on a Roll [04/24/2006]

How many feet of paper are on a roll of paper with a diameter of 48" if the core has a diameter of 4" and the paper is 0.014" thick?

Calculating the Diameter of a Carpet Roll [9/24/1995]

How do you calculate the diameter of a carpet roll when you have the length and the thickness?

Calculating the Length of String on a Reel [12/07/2001]

Is there a formula for calculating the length of wire that can go on a reel (spindle) where the reels may have different diameters, hub diameters, and widths, and the wires may have different diameters?

Calculus Cylinder-Cone Problem [07/13/1999]

I have to find the altitude of a triangle...

Circle of Radius 1 km around Given Latitude/Longitude [08/27/2002]

I need feed points for a circle of radius 1 km with center at a given latitude and longitude. Eight or more points should be enough for the program.

Circles of More than 360 Degrees [11/10/2001]

What shape is formed if one cuts along the radius of a circle and adds degrees by adding a sector?

Circumference at a Given Latitude [01/26/2001]

How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude?

Circumference of a Tube [10/11/2001]

What effect does the thickness of a tube have on the circumference when it's formed into a circle?

Comparing Volume and Surface Area [05/01/2002]

Why is it that the surface area of a given rectangular solid can sometimes be greater than the volume of that solid?

Complex Shapes [11/3/1994]

Please describe how to come up with mathematical "descriptions" for complex shapes (torus, witches hat, etc.) using three-dimensional math.

Compound Angles [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...

Cone Frustum [08/31/2001]

I am trying to calculate the height of a right frustum cone knowing only r, V, and the angle of the side.

Cone Symmetry [7/17/1996]

Why does a circular cone have infinite lines of symmetry?

Cone Volume [04/19/1999]

A right circular cone is circumscribed about a sphere of radius R cm. Find the ratio of the altitude to the base radius of the cone of largest possible volume.

Conical Sections [08/02/1999]

I know the angle and the diameter of one end of a frustum of a cone and the length of the frustum. What is the diameter of the other end of the frustrum?

Conical Vertex? [03/27/2003]

What is the point at the tip of a cone called?

Connection Between Circumference and Surface Area [05/08/1998]

Can you explain the connection between the circumference of a circle and the surface area of a sphere?

Constructing a Sphere out of Paper [02/08/2003]

I'm working on a school project and can't seem to find the answer anywhere. The assignment is to construct a 3D 9'-diameter sphere out of paper.

Container Height and Volume [08/01/1997]

A container's height is increased by 4 cm, and the length and width remain the same. If this change increased the volume by 12 percent, what was the original height of the container?

Copies of U.S. on Surface of Earth [11/07/2001]

I need to determine the number of identical copies of the continental United States that would fit on the surface of the Earth.

Cross-Section of a Prism [08/02/2001]

Please define cross section, and explain the formula for the volume of a prism.

Cube in a Cone [12/17/2002]

I need to find the length of each side of the cube.

Cubic Footage of a Tapered Log [08/07/2002]

Is there an equation that will calculate the cubic footage of a log given the diameters of each end and the length?

Cups and Volume [12/06/2001]

How can I calculate the volume of a box, if I know how many cups of rice fill it? And how can 2 cups be a volume measure?

Cutting a Cake into 8 Pieces with 3 Cuts [09/08/2002]

How do you cut a cake into 8 pieces making only 3 cuts? How do you cut a doughnut into 12 pieces with only 3 cuts?

Cutting a Cylinder out of a Sphere [02/25/1999]

What is the remaining volume after a cylinder of length 6" has been cut through the centre of a sphere?

Cutting a Sphere [02/18/1999]

How can I cut a sphere into an odd number of pieces?

Cutting a Wedge out of a Disk to Make a Cone [12/05/2005]

A cone can be formed by cutting a wedge out of a disk and then rolling the remaining part into the cone shape. How can I determine how big the wedge should be to make a cone of given dimensions?

Cylinder Height, Area, Volume [04/07/2003]

Why does the volume of a cylinder get larger as the radius gets larger and the height gets smaller?

Cylinder of Arbitrary Axis [9/2/1996]

What is the equation of a cylinder about an arbitrary axis...?

Daylight Hours and Latitude [1/9/1995]

How does the number of daylight hours on a given day of the year depend on latitude?

Defining an Ellipse [07/16/2003]

A right cylinder of radius 'r' (a lift duct) intercepts a plane (the deck of a hovercraft) at an angle of 30 degrees to the vertical. How may the resulting ellipse be scribed? - i.e., how do I mark the hole to be cut in the deck?

Defining Distance Mathematically [10/16/1996]

What is wrong with D' = sqrt(X^2 - X'2)?

Definition For Cylinder without Big Words [11/03/1998]

I just need a good definition for cylinder that I can understand.

Definition of a Cone [07/13/2000]

I don't see how a right circular cone cut parallel to the axis of symmetry reveals a hyperbola. Shouldn't it be a parabola?

Definitions of Cones and Cylinders [03/02/2004]

Are cones and cylinders pyramids, prisms or neither? My 5th grade geometry class cannot reach an agreement on this subject!

Definitions of Edge and Face in 2D and 3D [10/10/2008]

What is the 'official' definition of 'edge'? Specifically, is an edge restricted to the intersection of two non-coplanar faces or do two- dimensional shapes have edges? I'm also curious about a definition of 'face'. How many faces does a two-dimensional shape have?

Degrees in a Sphere? Steradians [09/27/2001]

If one can say that a circle contains 360 degrees, how many degrees can one say are in a sphere?

Depth of a Tank [09/04/1997]

A tank 100' long and 10' wide holds 15,000 cu. ft. of water...

Derivation of Geometric Formulas [5/29/1996]

What are the formulas for the surface area, total surface area, and volume of a sphere, and volume of a pyramid and cone?

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