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?
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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) (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
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The area of the circle (with radius 5) is square inches.
The area of the square is square inches.
The height of the cylinder (with base area square inches) is 12 inches, so the volume of the cylinder is
cubic inches.
The height of the prism (with base area 50 square inches) is 12 inches, so the volume of the cylinder is
cubic inches.
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