Find the volume of the body obtained by rotating the rectangle around the side equal to 5 cm if the diagonal is 13.

Let’s call our rectangle ABCD, where AB = CD = 5 cm, BC = AD. Consider the triangle BAD (angle A = 90 degrees), find the side AD, as the leg of a right-angled triangle:
AD ^ 2 = BD ^ 2 – AB ^ 2;
AD ^ 2 = 169 – 25;
AD = 12 cm.
When the rectangle rotates around AB, we get a cylinder, where AB is the height, we find the area of the base;
S = nR ^ 2 = n * 12 ^ 2 = 144n cm2.
Then the volume of the resulting body:
V = AB * S = 5 * 144p = 720p cm3.
Answer: the volume of the resulting body is 720p cm3.