Posted by **Charles** on Saturday, August 6, 2011 at 7:18am.

What is the volume of a spherical dome with radius 5.5ft and height 3.5ft?

- calculus -
**bobpursley**, Saturday, August 6, 2011 at 8:36am
Hmmm. Exactly what is height? Is this a truncated sphere?

- calculus -
**Reiny**, Saturday, August 6, 2011 at 8:58am
The way I read this:

A spherical cap is cut off giving a truncated sphere as bobpursley suspected.

Look at

http://en.wikipedia.org/wiki/Spherical_cap

to see how we can find the volume of that cap.

Volume = (πh/6)(3a^2 + h^2) , where a is the radius of the circular base of the cap, and h is its height.

To find a, look at a cross-section, and

a^2 + 2^2 = 5.5^2

a^2 = 26.25

and our h = 3.5

volume of cap = (3.5π/6)(3(26.25) + 3.5^2)

volume of whole sphere = (4π/3)(5.5^3)

subtract the volume of the cap from the volume of the sphere.

I will let you do the rest of the button-pushing.

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