The diagonal of the axial section of the cylinder is 13 cm and forms an angle with the base of the cylinder, the cosine

univerkov | July 9, 2021 | education

The diagonal of the axial section of the cylinder is 13 cm and forms an angle with the base of the cylinder, the cosine of which is 12-13. Find the volume of the cylinder.

The axial section of the cylinder is rectangle ABCD. The AC diagonal forms a right-angled triangle ACD, in which SinCAD = CD / AC = 12/13.

СD = 12 * 13/13 = 12 cm.

According to the Pythagorean theorem, we determine the length of the AD leg.

AD ^ 2 = AC ^ 2 – CD: 2 = 169 – 144 = 25.

AD = 5 cm.

Then the radius of the cylinder is R = АD / 2 = 5/2 = 2.5 cm.

Determine the volume of the cylinder.

V = π * R: 2 * h = π * (АD / 2) ^ 2 * СD = π * 6.25 * 12 = π * 75 cm3.

Answer: The volume of the cylinder is π * 75 cm3.

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