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Volume of the Sphere

Date: Fri, 4 Nov 94 21:06 NZDT
From: Joy

Dear Dr. Maths
I am an eighth grader. I am having difficulty with maths.
Could you please tell me what the volume of a sphere is. How
can I calculate it.
Thank you.

Date: Fri, 4 Nov 1994 08:13:05 +0900

Hi Joy-

Thanks for writing.  The volume of a sphere can be calculated as long
as you know the radius of the sphere - call it r.  Then the volume is
(4/3)*pi*r^3.  That is four thirds times pi times r cubed.
Have you worked on volumes of other solids yet?  In general the volume
of any cone or pyramid (a 3-d solid that has a two-d base, like a 
square, triangle, or circle and a point not on the plane that the base 
figure is connected to, like the Egyptian Pyramids or an ice cream cone)
is the area of the base times 1/3 of the height.

As it turns out this is related to the volume of a sphere.  Consider the
cone whose base is the same size as the circumference of the sphere at
its largest point and with height equal to the radius of the sphere.  In
other words, this cone would "fit inside" of the semi-sphere.  From the
formula I mentioned above, the volume of the cone is (1/3)*r*area of the
base.  The area of the base is the area of a circle with radius r: pi*r^2.  
So the volume is (1/3)pi*r^3.  This is exactly half of the volume of the 
semi-sphere.  If you add them together, you get (3/3)pi*r^3 = pi*r^3, 
which is the volume of a cylinder with radius r and height r.  Can you 
picture this?

What do you think?  Please write back if you have more questions about 
this or some other topic.

-Margaret, MD on call.
Associated Topics:
Middle School Higher-Dimensional Geometry

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