# 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 # 16 #, the cap's height is #8 #, and the cap's radius is #5 #. What is the object's volume?

##### 1 Answer

I would review my answer myself and trace bugs, if any.

#### 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.

Note that the height 8 of the cap is greater than the radius 5 of the

sphere, of which this is a part.

From the dimensions of the opposite spherical cap,

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

its sphere,

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

The entire volume

V = volume of the whole sphere - volume of the opposite spherical

cap + volume of the rectangular cylinder below

Volume of the opposite 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,