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 hexagon

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Question 1178421: 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 ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "r" be the radius of the cylinder.


Then the side length of the hexagonal prism is "r", too.


The equation to find "r" is


    2%2Api%2Ar - 6r = 4 centimeters,  or


    6.28r - 6r = 4


         r     = 4%2F0.28 = 14.286 cm.


From this point, complete the solution on your own.

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The key part of the problem just solved and explained.

The rest is a routine job to keep your mind active.


Happy calculations (!)