SOLUTION: A square prism is inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What are the volumes of the prism and the cylinder?

Algebra ->  Volume -> SOLUTION: A square prism is inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What are the volumes of the prism and the cylinder?      Log On


   

Question 622521: A square prism is inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What are the volumes of the prism and the cylinder?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that from above you just see the bases of the prism and the cylinder, looking like a square inscribed in a circle, like this:
The diameter of the circle is 10 inches, the length of the diagonal of the square.
Two sides of the square, of length x inches, form a right triangle with the diagonal for a hypotenuse, so
x%5E2%2Bx%5E2=100 --> 2x%5E2=100 --> x%5E2=50 --> x=sqrt%2850%29=sqrt%2825%2A2%29=sqrt%2825%29%2Asqrt%282%29=5sqrt%282%29
The area of the circle (with radius 5) is pi%2A5%5E2=25pi square inches.
The area of the square is x%5E2=50 square inches.
The height of the cylinder (with base area 25pi square inches) is 12 inches, so the volume of the cylinder is
25pi%2A12=highlight%28300pi%29 cubic inches.
The height of the prism (with base area 50 square inches) is 12 inches, so the volume of the cylinder is
50%2A12=600 cubic inches.