Deinonychus A.
asked • 07/23/20Geometry question. I think I got the answer, but I don’t know if it’s correct.
A cylindrical hole has been drilled through the center of a regular pentagonal prism. The base edge of the pentagon is 18 cm, the height of the prism is 16 cm and the radius of the hole is 2 cm. Determine the
volume of the solid to the nearest tenth.
I used the formula for finding a pentagonal prism, but the number is definitely wrong, and my work went downhill from there, so I’m looking for an accurate answer and correct steps.
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1 Expert Answer
If the side of the regular pentagon is 18 cm, then the Apothem = 18/(2*tan(36)) = 9/tan(36) = 12.4 cm.
The perimeter = 5 * 18 cm = 90 cm
Area of regular pentagon = 1/2 * Apothem * Perimeter = 558 cm^2.
The volume of the pentagonal prism = 558 cm^2 * 16 cm = 8928 cm^3
Volume of cylinder = PI * R^2 * H = 3.14 * 4 * 16 = 201 cm ^3.
The volume of the prism with the hole drilled is 8928 cm^3 - 201 cm^3 = 8727 cm^3
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Mark M.
Which formula did you use?07/23/20