Question

Total surface area of a cylinder having base radius “r” and height “h” is equal to __________

(a) 2πrh + 2πr^2

(b) 2πr^2

(c) 2πrh

(d) 4πr^2

The question was posed to me in a job interview.

The question is from Surface Area of a Right Circular Cylinder in chapter Surface Areas and Volumes of Mathematics – Class 9

Answer 1

Correct choice is (a) 2πrh + 2πr^2

For explanation I would say: Total surface area of a cylinder = curved surface area + 2 * area of the circular base

If we unfold the cylinder given in the above figure, the area of the rectangle gives us the area of curved surface area of a cylinder (As shown in the figure below).

One side of the rectangle is equal to “h” and the other side is equal to perimeter of circular edge of the cylinder, i.e. “2πr”.

Hence, the curved surface area of the cylinder = 2πr * h

= 2πrhArea of circular base = 2πr^2

Hence, total surface area of a cylinder = curved surface area + 2 * area of the circular base

= 2πrh + 2πr^2.