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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Changing Angle of a Tank [06/11/2003]

Points A and B represent pressure sensors in fixed positions on the base of a round tank. The chord through CD represents the water level in the tank. Lines a and b are the heights of water registered by each sensor...

Cones, Pyramids: Surface Area and Volume Formulas [03/11/2003]

How do you get the formula for surface area and volume for cones and pyramids?

Coordinate Systems, Longitude, Latitude [04/19/1997]

Can you explain pitch, roll, and yaw to me? Are there other systems for measuring an object's position in space?

Does a Cone have an Edge? A Vertex? [03/12/2002]

Our 4th grade math textbook defines a cone as "A solid figure with one circular face and one vertex." This sounds reasonable until you read the textbook's definitions for face, edge, and vertex.

Fourth Dimension [05/13/1997]

Can you help me understand the fourth dimension?

HyperCubes [3/21/1996]

Do you folks know of any videos that show the hyper-cube in action that would be appropriate for the high school level?

Is a Sphere 2-D or 3-D? [8/8/1996]

Is a sphere a two- or a three-dimensional object?

Number of Cylinder Edges [04/01/2002]

My son was asked "how many edges are there on a solid cylinder?" on a recent math examination. His answer was "2" and it was marked incorrect.

Three-dimensional Plane Diagrams [03/10/1999]

Draw: two parallel planes with another plane intersecting them; two parallel planes with an intersecting line.

Volume equations for a sphere and pyramid [6/10/1996]

I am now thoroughly confused: we just learned the formulas for volume of a sphere and volume of a pyramid, but, he wouldn't tell me how to do it.

Volume of a Pyramid [05/16/1999]

Can you give a step-by-step proof for the volume of a pyramid?

3D Figures and Intersections [03/04/1999]

Determining whether a line and plane intersect, and where, using vectors.

3D Geometry [11/17/1997]

You can draw a line of minimum distance between and perpendicular to two lines in 3space. I know how to get the distance and direction of this line, but I want to locate the line in 3space so that I can find its midpoint.

A 3-D Object that Fits 3 Holes [06/03/1999]

How can I make an object that can fit in 3 holes of different shapes, blocking all light, and sliding all the way through without forcing it?

3-D Shape That Can Be a Circle, Square, or Triangle in 2-D [09/08/2006]

Is there a shape that can fill and pass through a circular hole, a square hole, and a triangular hole?

The 4th Dimension [2/10/1996]

In my Geometry class we read the book, Sphereland . I couldn't visualize Overcubes and Overspheres. Even though I know we really shouldn't be able to see 4D figures, just as 2D creatures can't visualize 3D creatures, is there any way you could describe an oversphere?

Adding a 6-Inch Layer of Gravel [03/13/2003]

Your company is constructing a soccer field for a high school. The field is 110 yards long and 80 yards wide...

Angle Between Two Points on the Globe [7/17/1996]

Given their longitude and latitude, how can you determine the angle in radians between two cities?

Angle Between Two Sides of a Pyramid [10/29/1999]

How can I compute the angle formed by two sides of a frustrum of a pyramid?

Area and Volume of a Football [3/28/1995]

How would one find the area of a football? Or then again, how would one find the volume of a football?

Area and Volume of a Pear [6/4/1996]

How do you find the area and volume of a pear?

Area and Volume of Cuboid [09/09/2002]

How can I find the new volume and surface area of a cuboid after its volume has been reduced by 10%?

Area of a Cone [11/5/1994]

What is the area of a cone when given the height and the angle at the convergence point?

Area of a Pentagonal Pyramid [11/16/1995]

I would like to know the area of a pentagonal pyramid. The dimensions of the sides of the base are 5cm ea. and the height is 23cm.

The Area of a Roof [05/18/2002]

How can I determine the area of a hipped roof for a building 100 feet long and 80 feet wide, with a pitch of 6/12, and 3 feet of overhang for the eaves?

Area, Volume of a Cone [6/4/1996]

What are the formulae to find the volume and area of a cone?

Bases and Faces [12/05/2001]

I can't figure out the difference between a base and a face on the shapes we are learning.

Bearing Between Two Points [12/19/2001]

Is there an easy way to calculate the "heading" (relative to North=0) between two coordinates?

Bearing Calculation [09/01/1997]

Given two cities at geographic coordinates (xA,yA) and (xB,yB), is there a formula to calculate the bearing from city A to city B?

Beyond the Third Dimension [5/16/1996]

I am searching for information on 'beyond the third dimension'.

Beyond Three-Dimensional Geometry [06/17/2001]

If the first dimension is a line and the second dimension is a flat figure, the the third dimension is, say, a cube, then what is the fourth dimension? What is the fifth dimension?

Board Feet from a Log [03/19/2003]

What is the board feet of a 10-foot log if the diameter is 16 inches at one end and 14 inches at the other end?

Box for a Ball [09/26/2002]

The volume of a ball is 36pi cm^3. How do I find the dimensions of a rectangular box that is just large enough to hold the ball?

Bricks to Cover a Steeple [08/23/1997]

How many 6"x12" bricks would it take to cover an octagonal steeple with a diameter of 130 ft. and a height of 370 ft?

Building a Cone [01/28/2002]

I am trying to draw cone (frustum) with a larger radius size.

Building a Cone [10/28/2001]

I am trying to find a formula for building a cone for a chimney flashing. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2".

Building a Manger [12/03/2001]

Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

Building a Skateboard Ramp [9/19/1995]

I'm trying to build a skateboard ramp, pyramid with flat top, height one foot, angle of ascent thirty degrees, other angles ninety degrees and sixty degrees.

Building a Wooden Square-Based Pyramid [01/26/2001]

I want to build a wooden pyramid with a square base 8"by 8".

CADAEIBFEC and Other NCTM Questions [10/27/1998]

CADAEIBFEC is a mnemonic for an important piece of mathematical information. What is it?

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