Question

In case of a right circular cylinder the radius of base and height are in the ratio $2:3$. Therefore, the ratio of lateral surface area to the total surface area is

• A. $5:3$
• B. $3:5$
• C. $2:5$
• D. $2:3$

Answer 1

The correct option is B $3:5$

Let the base be $2a$, height be $3a$
Curved Surface
Area of a Cylinder of Radius "r" and height "h" $=2\pi rh$
Hence, CSA of the given cylinder $=2\pi \left(2a\right)\left(3a\right)=12\pi a^2$

Total Surface Area of a Cylinder of Radius "R" and height "h" $=2\pi R(R+h)$
Hence, TSA of the given cylinder $=2\pi \left(2a\right)(2a+3a)=20\pi a^2$
Required ratio $=12\pi a^2:20\pi a^2$
$12:20$
$3:5$