calculus
posted by Charles on .
What is the volume of a spherical dome with radius 5.5ft and height 3.5ft?

Hmmm. Exactly what is height? Is this a truncated sphere?

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 crosssection, 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 buttonpushing.