SOLUTION: `a right regular hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. the difference between the circumference of the circle and the perimeter of hexago

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Question 1178450: `a right regular hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. the difference between the circumference of the circle and the perimeter of hexagon is 4 cm. determine the volume of the prism.'
Answer by greenestamps(13209) About Me  (Show Source):
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In a regular hexagon inscribed in a circle, the side of the hexagon is equal to the radius of the circle. Let that length be r.

The circumference of the circle is (2pi)r; the perimeter of the hexagon is 6r.

The difference between the circumference of the circle and the perimeter of the hexagon is 4cm:

%282pi%29r-6r+=+4

Solve that equation for r; keep several decimal places of accuracy.

The volume of the prism is the area of the base, multiplied by the height. The height is 20 cm; the area of the base is 1.5%2Asqrt%283%29r%5E2.

Use the value of r you found to find the volume.