Question

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

• A. $2\pi r^2+\pi rh$
• B. $2\pi r(r+h)$
• C. $2\pi r^2(1+h)$
• D. $2\pi r^2+\pi r^{2}h$

Answer 1

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


When the right circular cylinder is cut open, the total surface area is the sum of the areas of 2 equal circles and 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 $=2\pi r\times h$
$\text{Surface Area}=\pi r^2+\pi r^2+2\pi rh\Rightarrow \text{Surface Area}=2\pi r^2+2\pi rh\Rightarrow \text{Surface Area}=2\pi (r^2+rh)\Rightarrow \text{Surface Area}=2\pi r(r+h)$