Ask Dr. Math

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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Spreading Mulch on a Garden [05/15/2000]

If there are 4 cubic yards of mulch in a yard, and the mulch is to be laid 3 inches thick, how many square feet can you cover?

Square Feet [4/13/1996]

I need to know how to compute square feet for some cabinets that I have to move in a room.

Surface Area and Volume: Cubes and Prisms [05/27/1998]

What is the definition of surface area and volume? What are the differences and similarities between surface area and volume?

Surface Area and Volume of Cylinders [05/25/2001]

How do you find the surface area and volume of a cylinder?

Surface Area of a Box [03/06/2003]

How do you find the surface area of a box?

Surface Area of a Cylinder [11/22/1997]

Is there any difference between the formula for an unrolled cylinder and the regular surface area formula for a cylinder?

Surface Area of an Egg [07/20/2002]

How do I find the surface area of an egg?

Surface Area of a Rectangular Solid [09/21/1999]

Can you find the surface area of a cube or other 3D rectangular object by calculating the area of the sides you can see and multiplying by 2?

Surface Area of a Sphere [03/25/1999]

How do I calculate the surface area of a sphere?

Surface Area of Blocks Glued Together [09/09/2001]

Three cubes whose edges are 2, 6, and 8 centimeters long are glued together at their faces. Compute the minimum surface area possible for the resulting figure.

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?

Tesseracts and Hypercubes [05/22/1997]

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

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

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

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?

Topology [05/10/1997]

What is topology? What is knot theory?

Topology [03/19/2001]

What is topology?

True and Magnetic North [04/08/2002]

How do you convert from true north to magnetic north?

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.

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 of a Cone [5/9/1996]

How much coffee can a tapered coffee pot hold?

Volume of a Cylinder [7/30/1996]

What is the volume of the storage tank with a diameter 6m, height 5m?

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 Sphere [05/19/2002]

Where does the (4/3) come from in the formula for the volume of a sphere?

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 Pyramid With Square Base [9/14/1996]

What is the volume of a pyramid with a a height of 20.6 meters and a square base with sides of 35 meters?

Volume vs. Capacity [05/01/2002]

Can you explain the difference between the terms volume and capacity? Also mass and weight.

Weight of a Whale [05/24/1999]

How do you find the weight of a whale?

What is a Torus? [11/30/1999]

Is there a good way to describe a torus to a child?

What is Geometry For? [03/01/2002]

What is geometry really for?

What is the Volume of this Tank? [3/22/1995]

What is the volume of a tank 10 feet in diameter, 8 feet deep, with a 2 foot conical bottom?

What Skew Lines Are and Aren't [01/14/2004]

A description of skew lines including diagrams and definitions.

When Does 2D Become 3D? [01/20/2003]

Is a piece of paper a 3D object when held up in space? Or is it a 2D object in 3D space?

Why Cubed? [11/27/2001]

Why do we use "cubed" for the volume of a figure?

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