A rectangle with a diagonal of 13 cm and one side of 5 cm rotates around the larger side.

A rectangle with a diagonal of 13 cm and one side of 5 cm rotates around the larger side. Find the volume and total surface area of the body of revolution.

First, we find the unknown side of the rectangle, denote it by x, using the rule that the sum of the squares of the sides is equal to the square of the diagonal:

x ^ 2 + 5 ^ 2 = 13 ^ 2;

x ^ 2 = 169 – 25 = 144;

x = √144 = 12 cm.

The side found, 12 cm, is the height of the cylinder (the body of revolution formed by the rectangle). And, known from the condition, the smaller side, 5 cm, is the radius of the body of revolution. Let’s find the volume of the cylinder:

V = P * 25 * 12 = 300P = 300 * 3.14 = 942 cm3.

And we will find its area:

S = 2P * 5 * 12 = 120P = 120 * 3.14 = 376.8 cm2.