3D and higher
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Dr. Math FAQ:
3D and higher
Browse Middle School 3D and Higher Geometry
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Selected answers to common questions:
Do cones or cylinders have edges?
- Finding the Amount of Cement Needed to Fill an Area [11/1/1995]
I have an area 16 feet by 16 feet and two inches deep. One 80-lb. bag
makes 2/3 cubic feet of cement. How many bags do I need to fill it?
- Finding the Volume of a Pyramid or Cone [05/09/2002]
I just don't get how to find the volume of a pyramid or a cone.
- Finding the Volume of a Trash Bag [2/12/1996]
How can you find the volume of a trash bag? I have to have a bag that is
3 cubic feet.
- Five Equal Pieces of a Square Cake [05/22/2001]
Ravina wants to cut a square cake using straight vertical cuts to make
five pieces of equal volume. If she makes the first cut from the cake's
center to the top left corner, where must she make the other cuts if they
all start from the cake's center?
- Front, Side, and Top Views [11/22/2003]
I'm having trouble explaining to my 7th grade students what the terms
'front view', 'side view', and 'top view' mean.
- Geometry Books [4/17/1996]
I am having trouble finding an instructive book on geometry. Do you have
- Geometry Project [11/1/1994]
Think of three examples of geometry in the real world, one non-man-made (found in nature).
- Helpful Ways to Remember Cylinder and Prism Formulas [03/28/2005]
I was wondering if you could tell me an easy way to memorize formulas
like volume, surface area, and lateral area for cylinders and prisms?
- How Many Dimensions Are There? [03/29/2001]
How do we know how many dimensions there are? What is the significance of
drawing 4D hypercubes? If I were in a 2D world, how would I be able to
represent 3D objects?
- Intersecting Lines Coplanar? [08/23/2002]
Do two intersecting lines have to be coplanar?
- Intersection of Two Planes [8/3/1995]
What is the Intersection of Two Planes?
- Is a Curved Surface a Face? [03/19/2008]
Is a curved surface a face or not? Like in a cylinder, is the curved
surface considered a face?
- Is a Sheet of Paper a 2D or 3D Object? [05/17/2008]
Our teacher said that a piece of paper is a two-dimensional object
that has no height, but some of my classmates and I disagree. We think
a piece of paper still has a height, even if it is very, very, small,
and that it is therefore a three-dimensional object. Who's right?
- Jobs That Use Geometry [12/18/2001]
I would like to learn how geometry is used in real life. What jobs
- Lateral Surface of a Cone [02/10/1999]
How do you find the formula for the lateral surface of a right cone?
- Length or Width? [12/02/2003]
Can you please explain the difference between height, length, width
and depth? Is it always the same for each thing?
- Math in soccer [05/21/1999]
How is math involved in soccer?
- The Meaning of Space [07/23/1997]
Is the term 'Space' a mathematical object? I have seen it in "Vector
Space," "Banach Space," and "Hilbert Space," but are they the same thing?
- Measuring the Circumference of the Earth [08/16/1999]
How did Eratosthenes use a mathematical formula to prove the earth is
- Metric Conversions [01/16/1997]
How do I convert cubic yards to cubic meters?
- Mobius Strips, Spheres, and Dimensionality [05/28/2003]
Is a Mobius Strip 2-D or 3-D? Or is it 1-D? What about a sphere?
- Moebius Strip [5/24/1996]
What would happen if you cut a moebius strip in half lengthwise?
- Moebius Strips: How Many Sides and Surfaces? [10/18/2001]
What is the difference between a side and a surface?
- Names of Parts of a Cone [8/2/1996]
Are the components of a net of a cone called faces in all cases, or only
- One Degree Latitude, Longitude: How Many Miles? [04/02/2002]
Approximately how many miles are there in one degree of longitude and one
degree of latitude in the states of Kansas and Oklahoma?
- Opposite Point on a Globe [11/08/1999]
What is the farthest place on earth from Atlanta, Georgia?
- Pappus' Centroid Theorem [06/05/2003]
What is the formula for the volume of a circular torus?
- Parallel Curves [05/21/1997]
If line segments can be parallel, can curves be parallel? Are lines of
- Parallel Lines [12/31/1998]
What are some ways of proving lines parallel - geometrically and
- Parts of a Cone [04/18/2001]
Does a solid cone have any edges?
- Proportions of Exact Enlargements [03/18/1998]
How are two objects related if one is an "exact enlargement of the
- Pyramids and Triangular Prisms [05/09/2000]
What's the difference between a pyramid and a triangular prism?
- Radius of a Sphere [01/29/1998]
What is the ratio of the areas and volumes of two spheres, one with
radius 3 times the other? What possible theorems are suggested?
- Radius of a Tennis Ball [04/03/2001]
How can we find the radius of a tennis ball without cutting it open?
- Ratio of Volume to Surface Area in Humans [12/09/1999]
What is the healthy ratio of volume to surface area for humans?
- Ratios and Geometry [10/29/1998]
An airplane flying at 33,000 feet has a visibility of 100 miles. What
percent of the total land area to the horizon is visible?
- Rectangular Prism [9/10/1995]
What is the term for a 3-dimensional rectangle, i.e., box?
- Relative Motion on Face of Earth [05/06/2007]
If I am traveling along the earth's surface at the same rate of speed
that the earth is rotating in the opposite direction then would I
appear to not be moving if you watched me from space?
- Rhumb Lines and Great Circle Routes [09/24/1998]
Can you explain great circles and rhumb lines and how they relate to
shortest distances in geometry?
- Sphere Formulas [03/26/1997]
What are the formulas for area and volume of a sphere?