Math Help - [SOLVED] Prism and Cylinder

Hey,

This is on page 19 # 32 of the Barron's SAT Math II Book.

If a square prism is inscribed in a right circular cylinder of radius 3 and height 6, the volume inside the cylinder but outside the prism is

a) 2.14
b) 3.14
c) 61.6
d) 115.6
e)169.6

Can you please show the steps cuz i really dont get this question. Thanks in advance!!!!

Hello, fabxx!

If a square prism is inscribed in a right circular cylinder of radius 3 and height 6,
the volume inside the cylinder but outside the prism is:

. .

Visualize a right circular cylinder (a soup can).
A square-based block is fitted into the can snugly.
They both have the same height, 6.

The base looks like this:

Code:

              * * *
          *           *
        o - - - - - - - o
       *|             / |*
        |           /   |
      * |         /     | *
      * |     6 /      x| *
      * |     /         | *
        |   /           |
       *| /     x       |*
        o - - - - - - - o
          *           *
              * * *

The diameter of the circle is 6.
Let = side of the square.

From Pythagorus: .
. .


The volume is the cylinder is: .

The volume of the block is: .


Solution: . . . . answer (c)