Find the total surface area obtained by rotating a 6cm and 10cm rectangle around an axis

Find the total surface area obtained by rotating a 6cm and 10cm rectangle around an axis of symmetry parallel to the larger side

The body obtained by rotating the rectangle around the axis of symmetry is a cylinder. Based on this, the side of the rectangle, parallel to the axis, is its height, which is 10 cm, and its other side is 6 cm in diameter.

The total surface area of ​​the cylinder is equal to the sum of the lateral surface area and twice the base area:

Sp.p. = 2πrh + 2πr ^ 2.

Let’s calculate the radius of the base. Since the base diameter is 6 cm, and the radius is half of it:

r = d / 2;

r = 6/2 = 3 cm.

Sp.p. = (2 * 3.14 * 3 * 10) + (2 * 3.14 * 32) = 188.4 + 56.52 = 244.92 cm2.

Answer: the total surface area of ​​this body is 244.92 cm2.