You are given a hexagonal prism with a base side of 4 and a height of 4 / pi.
| May 13, 2021 | education
You are given a hexagonal prism with a base side of 4 and a height of 4 / pi. Find the volume of the cylinder inscribed in the prism.
Since the prism is hexagonal and regular, the radius of a circle inscribed in a regular hexagon is: R = a * √3 / 2, where a is the side of a regular hexagon.
R = 4 * √3 / 2 = 2 * √3 cm.
The height of the cylinder is equal to the height of the prism, h = 4 / π cm.
Determine the volume of the cylinder.
V = π * R ^ 2 * h = π * 12 * 4 / π = 48 cm3.
Answer: The volume of the cylinder is 48 cm3.
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