# The height of the cylinder is 5 cm, the diagonal of the axial section is 13 cm. Find the volume of the cylinder.

August 28, 2021 | education

| The height of the cylinder is perpendicular to its bases, then the ACD triangle is rectangular.

Let us define the legs AD in the triangle ACD by the Pythagorean theorem.

AD ^ 2 = AC ^ 2 – CD ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

AD = 12 cm.

Determine the radius of the circle at the base of the cylinder.

R = ОА = АD / 2 = 12/2 = 6 cm.

Determine the area of the base of the cylinder.

Sop = n * R ^ 2 = n * 6 ^ 2 = n * 36 cm2.

Determine the volume of the cylinder.

V = Ssc * CD = n * 36 * 5 = n * 180 cm3.

Answer: The volume of the cylinder is n * 180 cm3.