Question

A cylinder is inscribed inside of a square prism so that touches each face of the rectangle or prism. The empty space outside of the cylinder, but inside of the prism is to be filled with a liquid epoxy. If the cylinder has a circumference of 84.78 cm and the writing either prism is 40 cm tall, how many cubic centimeters of epoxy will be required to completely fill the empty spaces?

Answer 1

To solve take  (Volume of Prism) - (Volume of Cylinder) = Epoxy

V=(Area of base)(height) 

Both they Cylinder and prism have a height of 40 inches 
we can find the sides of the base of the prism by finding the diameter of the cylinder.

C=πd    so  84.78 = πd.

Divide both sides by Pi (3.14)
$\frac{84.78}{3.14} = 27$

Half of the diameter is the radius to find the area of the cylinder base. 27/2=13.5

The volume of Prism is found by
$V=l*w*h$

 27*27*40 = 29160 sq cm

The volume of cylinder is found by
$V= \pi r^{2}h$

using  $3.14* 13.5^{2}*40$ = 22890.6

29160 - 22890.6 = 6269.4 cubic centimeters