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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.


Resolving Pitch and Yaw [02/10/2003]

Resources on 3D Surface Plots [9/12/1995]
I would appreciate it if you would let me know of any databases or handbooks on the Internet for 3D surface plots of equations z=f(x,y,...).


The Role of Postulates [03/29/2003]

Roll of Paper [06/15/2003]
I am getting a paper rewinder that runs 6,000 ft a minute, and the roll is 50' high above the floor. How many miles and feet are there in this roll of paper and how long will it take to run?

Same Surface Area and Volume [03/28/2001]
How can I find two objects of the same type of shape with the same surface area but different volumes? For example, two rectangular prisms or two cylinders?

The Second Octant [04/03/2002]

Segment of an Ellipse [09/06/2001]

Setting Sun [5/19/1995]

Shared Points on Concentric Circles [03/11/2004]

Shortest Distance between Points [01/17/1998]

Similar Pyramids and Measurement Ratios [08/10/2002]
The volumes of two similar pyramids are 27 and 64. If the smaller has lateral surface area of 18, how would I find the lateral surface area of the larger one?

Sketching a Plane in Three Dimensional Space [11/15/2005]
I know that an equation like 2x + y + z = 3 represents a plane in three dimensions. How can I sketch that plane on the xyz axes? Also, how can I sketch a system of such equations to find the solution geometrically?

Skew Axis? Cue Pappus [07/19/2015]
How do you calculate the volume of a solid of revolution generated around a skew axis? Doctor Anthony leans on Pappus' Theorem.

Small Section of a Sphere [01/10/2002]
Find the volume and the areas of each of the surfaces/faces of a small section of a sphere with "dimensions" delta r, delta theta, delta phi, in spherical coordinates.

Spaces Formed by Intersecting Planes [07/19/1998]
Do you know of a proof that would be used to show how many spaces can be formed by the intersecting of five planes in space? n spaces?

Sphere Equation Variables [08/21/2001]
In the standard equation: r^2 = (x-h)^2 + (y-K0^2 + (z-l)^2 ...what do the points h, k, and l represent?

Sphere Eversion [8/11/1996]
How do you mathematically turn a sphere inside out?

Sphere Formulas [03/26/1997]
What are the formulas for area and volume of a sphere?

A Sphere in a Cube [3/23/1996]
I have a cube of 200x200x200 and a sphere with a radius of 100 is inside it. I want to be able to put in x and y and using a formula get z.


Sphere Surface Area Precision [04/22/2003]

Spherical Triangles [10/26/1996]


Surface Area and Volume Derivative [10/30/2000]

Surface Area and Volume of a Sphere [08/30/1999]
Besides using integration, is there an intuitive way of seeing why the surface area of a sphere = 4(pi)r^2 and the volume = (4/3)(pi)r^3?

Surface Area and Volume of a Sphere [05/16/2000]
Without using calculus, how can I show why the coefficient in the formula for the surface area of a sphere is 4, and why 4/3 is the coefficient in the formula for the volume of a sphere?

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 Cone [06/18/1998]
What is the formula for the surface area of a cone?

Surface Area of a Cylinder [9/25/1995]
What is the formula to calculate the surface of a cylinder with 25cm diameter and 20cm height?

Surface Area of an Egg [02/28/2001]
How do you find the surface area of an egg?

Surface Area of an Egg [07/20/2002]
How do I find the surface area of an egg?



Surface Area of a Right Circular Cone [9/5/1995]
Could you please tell me the formula for finding the surface area of a right circular cone?

Surface Area of a Right Cylinder [08/21/2001]
The problem in my book asked me to find the surface area of a right cylinder in centimeters with the dimensions given in meters.

Surface Area of a Sphere [10/03/1997]

Surface Area of a Sphere [04/10/1998]

Surface Area of a Sphere [03/25/1999]
How do I calculate the surface area of a sphere?


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