Find the volume of the body obtained by rotating a rectangle with sides of 6 cm and 8 cm around a straight

Find the volume of the body obtained by rotating a rectangle with sides of 6 cm and 8 cm around a straight line that passes through the midpoints of its smaller sides.

If we rotate the rectangle along the axis passing through the midpoints of its smaller sides, then we get a cylinder, at the base of which lies a circle with a radius equal to half the length of the smaller side of the rectangle, R = 3 cm, and a height equal to the length of the larger side of the rectangle, h = 8 cm.

The volume of a cylinder is equal to the product of the area of the base and the height.

V = S main. * h; S main. = ПR ^ 2; V = ПR ^ 2 * h;

V = П * 3 ^ 2 * 8 = П * 9 * 8 = 72П (cm ^ 3); П = 3.14; V = 72 * 3.14 = 226.08 (cm ^ 3).

Answer. 72П cm ^ 3 or 226.08 cm ^ 3.