Question

The lateral surface of a cylinder is equal to the curved surface of a cone. If the radius be the same find the ratio of the height of the cylinder and slant height of the cone

• A. 1 : 3
• B. 1 : 4
• C. 1 : 2
• D. 1 : 5

Answer 1

Answer: (C)

1 : 2

Let r be the radius of both the cylinder and the cone
Again let h and l respectively be the height and slant height of the cylinder and the cone Then
lateral surface of the cylinder =curved surface of the cone
$\Rightarrow 2\pi rh=\pi rl\Rightarrow 2h=l$
$\Rightarrow \frac{h}{l}=\frac{1}{2}\Rightarrow h:1=1:2$