# Find the volume of a cylinder in which the diagonal of the axial section is 10 cm and the radius of the base is 4 cm.

August 28, 2021 | education

| The axial section of the cone is a rectangle ABCD, the AD side of which is the diameter of the circle at the base of the cylinder, and the AB side is the height of the cylinder.

Then AD = 2 * R = 2 * 4 = 8 cm.

In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg AB.

AB ^ 2 = BD ^ 2 – AD ^ 2 = 100 – 64 = 36.

AB = 6 cm.

Determine the volume of the cylinder.

V = Sbase * h = π * AO ^ 2 * AB = π * 16 * 6 = 96 * π cm3.

Answer: The volume of the cylinder is 96 * π cm3.

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