The area of the base of the cylinder is Q, the area of its axial section is S. Find the volume of the cylinder.
| June 24, 2021 | education
Knowing the area of the base of the circle at the base of the cylinder, we determine its radius.
Sb = π * R ^ 2 = Q cm2.
R ^ 2 = (Q / π) see.
R = √ (Q / π) see
Determine the diameter of the circle.
AD = 2 * √ (Q / π).
The axial section of the cylinder is a rectangle AВСD, then Ssection = AB * AD = S cm2.
AB = S / 2 * √ (Q / π) see.
Determine the volume of the cylinder.
V = Sax * AB = Q * S / 2 * √ (Q / π) = Q * S * √ (Q / π) / 2 * Q / π = S * √ (Q / π) / 2 / π = π * S * √ (Q / π) / 2 = S * √ (Q * π) / 2 cm3.
Answer: The volume of the cylinder is S * √ (Q * π) / 2 cm3.
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