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Browse High School Higher-Dimensional Geometry
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Selected answers to common questions:
Do cones or cylinders have edges?
Latitude and longitude.
MaximizIng the volume of a cylinder.
- Calculating How Much Paper Is on a Roll [04/24/2006]
How many feet of paper are on a roll of paper with a diameter of 48"
if the core has a diameter of 4" and the paper is 0.014" thick?
- Calculating the Diameter of a Carpet Roll [9/24/1995]
How do you calculate the diameter of a carpet roll when you have the
length and the thickness?
- Calculating the Length of String on a Reel [12/07/2001]
Is there a formula for calculating the length of wire that can go on a
reel (spindle) where the reels may have different diameters, hub
diameters, and widths, and the wires may have different diameters?
- Calculus Cylinder-Cone Problem [07/13/1999]
I have to find the altitude of a triangle...
- Circle of Radius 1 km around Given Latitude/Longitude [08/27/2002]
I need feed points for a circle of radius 1 km with center at a given
latitude and longitude. Eight or more points should be enough for the
- Circles of More than 360 Degrees [11/10/2001]
What shape is formed if one cuts along the radius of a circle and adds
degrees by adding a sector?
- Circumference at a Given Latitude [01/26/2001]
How can I calculate the circumference of a line around the earth (a
circle) at 40 degrees north latitude?
- Circumference of a Tube [10/11/2001]
What effect does the thickness of a tube have on the circumference when
it's formed into a circle?
- 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?
- Compass, Ruler, and Radius — of a Sphere [09/16/2016]
A recreational mathematician seeks help calculating the radius of a sphere using only
compass and ruler. After considering several approaches, Doctor Peterson cracks the
case by invoking some triangle geometry and the law of cosines.
- Complex Shapes [11/3/1994]
Please describe how to come up with mathematical "descriptions" for
complex shapes (torus, witches hat, etc.) using three-dimensional math.
- Compound Angles [01/14/2001]
A rail does not go into a post horizontally, but has a rise angle of 30
degrees and a side angle of 39 degrees. The hole to be routed needs to be
a parallelogram instead of a square...
- Cone Frustum [08/31/2001]
I am trying to calculate the height of a right frustum cone knowing only
r, V, and the angle of the side.
- Cone Symmetry [7/17/1996]
Why does a circular cone have infinite lines of symmetry?
- Cone Volume [04/19/1999]
A right circular cone is circumscribed about a sphere of radius R cm.
Find the ratio of the altitude to the base radius of the cone of largest
- Conical Sections [08/02/1999]
I know the angle and the diameter of one end of a frustum of a cone
and the length of the frustum. What is the diameter of the other end of
- Conical Vertex? [03/27/2003]
What is the point at the tip of a cone called?
- 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?
- Constructing a Sphere out of Paper [02/08/2003]
I'm working on a school project and can't seem to find the answer
anywhere. The assignment is to construct a 3D 9'-diameter sphere out
- Container Height and Volume [08/01/1997]
A container's height is increased by 4 cm, and the length and width
remain the same. If this change increased the volume by 12 percent, what
was the original height of the container?
- Copies of U.S. on Surface of Earth [11/07/2001]
I need to determine the number of identical copies of the continental
United States that would fit on the surface of the Earth.
- Cross-Section of a Prism [08/02/2001]
Please define cross section, and explain the formula for the volume of a
- Cube in a Cone [12/17/2002]
I need to find the length of each side of the cube.
- Cubic Footage of a Tapered Log [08/07/2002]
Is there an equation that will calculate the cubic footage of a log
given the diameters of each end and the length?
- 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?
- Cutting a Cylinder out of a Sphere [02/25/1999]
What is the remaining volume after a cylinder of length 6" has been cut
through the centre of a sphere?
- Cutting a Sphere [02/18/1999]
How can I cut a sphere into an odd number of pieces?
- Cutting a Wedge out of a Disk to Make a Cone [12/05/2005]
A cone can be formed by cutting a wedge out of a disk and then rolling
the remaining part into the cone shape. How can I determine how big
the wedge should be to make a cone of given dimensions?
- 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 of Arbitrary Axis [9/2/1996]
What is the equation of a cylinder about an arbitrary axis...?
- Daylight Hours and Latitude [1/9/1995]
How does the number of daylight hours on a given day of the year depend
- Defining an Ellipse [07/16/2003]
A right cylinder of radius 'r' (a lift duct) intercepts a plane (the
deck of a hovercraft) at an angle of 30 degrees to the vertical. How
may the resulting ellipse be scribed? - i.e., how do I mark the hole
to be cut in the deck?
- 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 Cone [07/13/2000]
I don't see how a right circular cone cut parallel to the axis of
symmetry reveals a hyperbola. Shouldn't it be a parabola?
- 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!
- Definitions of Edge and Face in 2D and 3D [10/10/2008]
What is the 'official' definition of 'edge'? Specifically, is an edge
restricted to the intersection of two non-coplanar faces or do two-
dimensional shapes have edges? I'm also curious about a definition of
'face'. How many faces does a two-dimensional shape have?
- 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...