A regular quadrangular prism with a volume of 24 cm3 is inscribed into a cylinder whose height
| August 3, 2021 | education
A regular quadrangular prism with a volume of 24 cm3 is inscribed into a cylinder whose height is 12 cm. Find the volume of the cylinder.
The height of the inscribed prism is equal to the height of the cylinder, then KH = AB = 12 cm.
The volume of the inscribed prism is equal to: Vpr = Sosnpr * KH.
Sopr = Vpr / KH = 24/12 = 2 cm2.
Since the prism is correct, there is a square at its base, then НМ = √2 cm.
From the right-angled triangle HPM, according to the Pythagorean theorem, HP ^ 2 = 2 * HM ^ 2 = 4.
HP = 2 cm.
Diagonal НР is the diameter of the cylinder base, then ОН = R = 2/2 = 1 cm.
Determine the volume of the cylinder.
Vcyl = π * OH ^ 2 * AB = π * 1 * 12 = 12 * π cm3.
Answer: The volume of the cylinder is 12 * π cm3.
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