The axial cross-sectional area of the cylinder is 16 cm ^ 2, the base area is 8 cm ^ 2. Calculate the height

univerkov | January 5, 2021 | education

The axial cross-sectional area of the cylinder is 16 cm ^ 2, the base area is 8 cm ^ 2. Calculate the height and lateral surface area of the cylinder.

The axial section of the cylinder is a rectangle AВСD, then Ssection = AB * AD = 16 cm2.
The BP segment is the diameter of the circle at the base of the cylinder.
Sb = π * R2 = π * AO2 = 8 cm2.
AO2 = 8 / π.
AO = √ (8 / π) cm.
The axial section area is equal to: Ssech = AD * AB = 2 * AO * AB.
Then AB = Ssech / 2 * AO = 16 / (2 * √ (8 / π) = 8 / √ (8 / π) cm.
Let us determine the area of the lateral surface of the cylinder.
Side = 2 * π * AO * AB = 2 * π * √ (8 / π) * 8 / (√8 / π) = 16 * π cm2.
Answer: The area of the lateral surface of the cylinder is 16 * π cm2.

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