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Middle School Archive

Browse Middle School 3D and Higher Geometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Do cones or cylinders have edges?

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Area and Volume [04/10/2002]

I cannot figure out how to do volume.

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.

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.

The Volume of a Cylinder [11/8/1995]

What is the formula for computing the volume of a cylinder?

Volume of the Sphere [11/4/1994]

I am an eighth grader. Could you please tell me what the volume of a sphere is? How can I calculate it?

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...

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

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

Area, Surface Area, and Volume: How to Tell One Formula from Another [01/18/1999]

Unit dimensions -- and even an idea from calculus -- can tell you which formula you're using.

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.

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

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

Circles and Squares [4/3/1996]

Given a large circle with a square inside it (the sides of the square are equal to the radius of the larger circle and are chords of the circle) and a smaller circle inside the square...

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?

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?

Converting Between Cubic Feet and Cubic Yards [05/09/2002]

How can I figure out how many cubic feet are in a cubic yard?

Cubic Centimeter, Cubic Inch [08/26/1997]

Can you help me define these terms?

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?

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 Volume [6/30/1996]

What is the formula for the volume of a cylinder?

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 Parellelepiped [9/18/1995]

What is a parallelepiped?

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!

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...

Diameter of the Base of a Cone [08/12/1998]

How do you find the formula to calculate the diameter of the base of a cone of nine degrees at various lengths?

Dimensions [08/30/2001]

What are 1-dimensional, 2-dimensional, and 3-dimensional? What's the difference?

Dimensions of a Cardboard Box [09/28/1997]

A box with a square bottom and a volume of 2000 centimeters can be made by cutting 5-centimeter squares from the corners of a piece of cardboard...

Distance Between Opposite Corners of a Box [05/09/2002]

A moth is sitting in the lower left front corner of a storage shed. What is the length of the shortest path that the moth can fly to the upper right back corner of the shed?

Does a Sphere have Sides? [04/20/2001]

How many sides does a sphere have?

Earth - an Oblate Spheroid [05/17/1999]

Where can I find real-life examples of an ellipsoid?

Edge of a Cube Given Volume [10/06/1997]

I am a teacher currently teaching volume to a class of Grade 5 pupils.

Edges vs. Corners [04/18/2002]

My students get confused on how to determine an edge versus a corner, and counting the number of edges on a geometric figure, say a cube.

Einstein, Curved Space, and Pi [10/09/1999]

If space is curved and Euclidean geometry doesn't apply, doesn't that mean that the value of pi changes and can sometimes be rational?

Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]

What are the origins and roots of the words geometry, algebra, and trigonometry?

Euclid's Parallel Postulate [2/14/1995]

We are studying Euclid's Parallel Postulate. Why did mathematicians disagree with him? What other geometries resulted from this disagreement? What postulate replaced the Parallel Postulate?

Explanation of the Formula for the Volume of a Pyramid [06/16/2005]

Can you explain WHY the formula for the volume of a pyramid is (base*height)/3?

Figuring Out Formulas for Area [08/24/1999]

How can I remember formulas for squares, triangles, cylinders, etc?

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