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 10, the cap's height is 7, and the cap's radius is 8. What is the object's volume?

1 Answer
Apr 20, 2018

833π+76803 cubic units.

Explanation:

This is a square prism. The radius of the cap is 8, so the width of the square is 16.

Volume of prism:

Area of base x height.

162×10=2560

Volume of a spherical cap is given by:

V=πh23(3rh)

V=π723(3(8)7)

V=π493(17)=833π3

Total volume:

833π3+2560=833π+76803 cubic units.