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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Surface Area of Cones and Pyramids [09/27/2003]

Can the method for finding the surface area of a pyramid be used as well to find the surface area of a cone?

Surface Area of Earth (a Sphere) [8/30/1996]

Could you tell me the formula for determining the surface area of a sphere?

Surface Area of Solid Figures [9/18/1995]

HELP!! My math teacher was talking today about the surface area of figures. I know about the area and how to find it, but I am confused about this.

Surface Areas of Soap Bubbles [11/30/1999]

If you build a frame shaped like a tetrahedron and dip it in bubble solution, why do all of the faces of the bubble collapse to a point in the middle of the tetrahedron?

Swimming Pool Volume [07/26/2001]

How many gallons will an above-ground 24-foot-diameter pool 48 inches tall hold?

Swimming Pool Volume [02/28/2002]

What formula would I use to calculate the volume in gallons of a swimming pool 135' x 70' with different depths of 3', 5', 8' and 11'?

Taping a Cylinder [01/29/2001]

If I want to wrap sticky tape around a cylinder to cover it, what is the relation between the diameter of the cylinder, the thickness of the tape, and the angle between the diameter of the cylinder and the length of the tape?

Tesseract [04/25/2001]

Why does a tesseract contain eight cubes?

Tesseracts and Hypercubes [05/22/1997]

Can you give me any good sources of information that a high school geometry student would understand?

Tetrahedron Projected on a Plane [10/29/1996]

How do you project a regular tetrahedron perpendicularly onto a plane to get the maximum area shadow?

Three-dimensional Counterparts for Two-dimensional Objects [03/04/1998]

Three-dimensional counterparts for lines, polygons, perpendicular lines, and collinear lines.

Three-Dimensional Vectors [01/29/2003]

I am finding it very hard to understand and visualise the notion of a vector in 3 dimensions.

Three Holes Puzzle [05/02/2002]

A piece of plywood has three holes it it: a circular hole with a diameter of 2 cm, a square hole with 2 cm sides, and a triangular hole with a base and height of 2 cm. What object could completely plug AND pass completely through each hole?

A Three-Legged Stool [06/26/2001]

Why is a three-legged stool steady, while a four-legged stool can be wobbly?

Three Pyramids in a Cube [03/04/2002]

How can three pyramids fit exactly into a rectangular prism?

Three Spheres in a Dish [08/04/1999]

What is the radius of a hemispherical dish if 3 spheres with radii of 10 cm are inside the dish and the tops of all 3 spheres are exactly even with the top of the dish?

Tic-Tac-Toe on a Torus [03/29/2001]

Can you make a tic-tac-toe game that won't end in a tie?

Tipped and Partially Filled Frustum [12/14/2003]

A vessel in a plant where I work is the frustum of a cone on its side. A liquid is contained in this section and pours out the end of the cone section, therefore the liquid only takes up a certain portion of the cone's volume. How can I compute the volume of the liquid?

Topology [12/31/1997]

Is there a simple definition for homeomorphism? for topology?

Topology [05/10/1997]

What is topology? What is knot theory?

Topology [03/19/2001]

What is topology?

Transformation between (x,y) and (longitude, latitude) [01/02/2002]

I have two questions on the transformation between (x,y) and (longitude, latitude).

Triangle Centroid in 3-Space [12/30/1996]

Given three points in 3-space that, when connected, form a triangle, what are the coordinates of the centroid?

Trigonometry in the Third Dimension [04/30/1998]

How does trigonometry change when we move into the third dimension?

True and Magnetic North [04/08/2002]

How do you convert from true north to magnetic north?

Two Interpretations of Dimensionality in Geometric Figures [03/16/2004]

A line is 1 dimensional, a square or rectangle is 2 dimensional, and a cube is 3 dimensional. My question is what if you throw in parabolas or circles or the absolute value function, etc.? A circle is kind of like a parabola, but it is very much like a square, so I am thinking it is 2-dimensional. My conclusion is that the only 1 dimensional object is a straight line, and a point is 0 dimensional, but I am not confident that I am correct. Can you please clear this up for me?

Two Polygons in 3D Space [01/31/2003]

How do you find the shortest distance between two polygons in 3D space?

Understanding Fourth Dimension Figures [07/05/1998]

Can you help me figure out the equations for fourth dimension figures such as the tesseract and the hypertetrahedron?

Union of Spherical Caps [09/10/2001]

Suppose I have two spheres of radius r1 and r2 respectively, and they partly overlap. What's the formula for the overlapping volume?

Units and Cylinder Volume [02/06/2003]

Find the volume and surface area of a cylindical storage tank with a radius of 15 feet and a height of 30 feet.

Unit Sphere [01/21/2002]

Is there such thing as a "unit sphere" that has to do with trigonometric functions and the placement of points on said sphere?

Using Geometry to Make a Roof [8/30/1995]

I'm not a student but a wood worker with a question on solid geometry. I want to know how to calculate the angle on the sides of triangles in order to form a cone shaped (not round but angular) roof.

Using Vectors in Geometry and Physics [07/10/1998]

How do you use vectors in problems about medians, areas, and acceleration and velocity?

Variable Volumes in an Oblate Spheroid [12/21/2002]

We need to know how much water is in the tank at any given time.

Vertices in a Prism [05/12/1999]

What is the formula for finding the number of vertices in a prism?

Visible/Hidden Sides on Stacked Cubes [12/12/2001]

Find a formula for the number of sides hidden/visible on cubes when put in different arrangements: a line; a double line; stacked three- dimensionally.

Visualizing a Klein Bottle [08/19/1999]

What part of a Klein bottle can't be seen or represented in 3D? Is there a technique that can help me visualize higher dimensions?

Visualizing Skew Lines [05/16/2002]

What do you call lines that are not parallel but don't intersect?

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?

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