# 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 lengths of the top. The prism's height is # 3 #, the cap's height is #7 #, and the cap's radius is #8 #. What is the object's volume?

##### 1 Answer

#### Explanation:

I use the formula:

Volume of the cone-ice like part of a sphere of radius a

where

cone, from the center of the sphere to the periphery of the cap.

From the dimensions of the opposite spherical cap,

the semi-angle that this opposite cap subtends at the center of

its sphere,

Here,

The side length of the square-top of the prism is

The entire volume

V = volume of the opposite spherical

cap + volume of the rectangular cylinder below

The volume of the spherical cap

= the volume of the con-

ice-like part of the sphere that has this cap as its top - volume of

the cone part. Now,