Question

Which among the following represents the total surface area of a right circular cylinder?

• A. $2\pi r^2+\pi rh$
• B. $2\pi (r^2+rh)$
• C. $2\pi r^2+\pi r^{2}h$
• D. $\pi r^2+\pi r^{2}h$

Answer 1

The correct option is B $2\pi (r^2+rh)$


When a right circular cylinder is cut open, the total surface area is the sum of the areas of 2 equal circles and the area of a rectangle as shown in the figure.

The area of circle $=\pi r^2$
The length of the rectangle is the circumference of the circle in case of right circular cylinder.

Therefore, the area of the rectangle shown in the figure $=2\pi r\times h$

$TotalSurfaceArea=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh=2\pi (r^2+rh)$