Question

An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is `9`, the cap's height is `2`, and the cap's radius is `4`. What is the object's volume?

Answer 1

`630.5`

Explanation:

The "tricky" part is really the sphere on top. The square dimension of the prism is also defined directly by the cap radius `(D = 2 xx r)`.
The base volume is simply `9 xx 8 xx 8 = 576`

The volume of the cap is : `V_c = 1/6 xx pi xx h xx (3 xx a^2 + h^2)`
`V_c = 1/6 xx pi xx 2 xx (3 xx 4^2 + 2^2)`

`V_c = 54.5`
TOTAL Volume `= 576 + 54.5 = 630.5`

http://mathworld.wolfram.com/SphericalCap.html