Acylinder 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?

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)


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


 27*27*40 = 29160 sq cm

The volume of cylinder is found by


using  = 22890.6

29160 - 22890.6 = 6269.4 cubic centimeters