A rectangle whose sides are 5:12 apart and a diagonal of 13 cm rotates around the larger side

A rectangle whose sides are 5:12 apart and a diagonal of 13 cm rotates around the larger side. Find the volume of the cylinder obtained by rotation.

Let the length of the smaller side of the rectangle be 5 * X cm, then the length of its larger side is 12 * X cm.

From a right-angled triangle AВD, according to the Pythagorean theorem, ВD ^ 2 = AB ^ 2 + BC ^ 2.

169 = 144 * X ^ 2 + 25 * X ^ 2.

X ^ 2 = 169/169 = 1.

X = 1.

Then AD= BC = 5 cm, AB = СD = 12 cm.

Then the radius of the cylinder is equal to AD = R = 5 cm, the height of the cylinder is equal to AB = h = 12 cm.

The volume of the cylinder is:

V = π * R2 * h = π * 25 * 12 = 300 * π cm3.

Answer: The volume of the cylinder is 300 * π cm3