A rectangle with a diagonal of 18 cm and inclined to the base at an angle of 30 degrees is the axial

A rectangle with a diagonal of 18 cm and inclined to the base at an angle of 30 degrees is the axial section of the cylinder. Find the total surface area of the cylinder.

Let us determine what the side of the rectangle will be equal to, which is at the same time the height of the cylinder, when it is known that the diagonal of the rectangle is 18 cm:

18 * 1/2 = 9.

Let’s define what the side of the rectangle will be equal to, which is at the same time the diameter of the base of our cylinder:

√ (182 – 92) = √ (9 * 27) = 9√3.

Then the radius of the base will be equal to:

9√3: 2 = 4.5√3.

Let us determine what the total surface area is equal to:

S = 2πr (r + h) = 2 * 3.14 * 4.5√3 (4.5√3 + 9) = 127.17 (3 + 2√3).

Answer: 127.17 (3 + 2√3).