Question

A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is \(\frac{15}{8}\)times the lateral surface area of the right circular cylinder. What is the ratio of radius to height of the cylinder ? 

(a) 3 : 4 

(b) 9 : 4 

(c) 15 : 8 

(d) 8 : 15

Answer 1

(b) 9 : 4

Let r and h be the radius and height of the cone and r and H be the radius and height of the cylinder.

∴ Volume of cone = \(\frac13\) πr²h 

Volume of cylinder = πr²H 

By the given condition, \(\frac13\) πr²h = πr²H 

⇒ h = 3H 

Lateral surface area of cone = πrl 

Lateral surface area of cylinder = 2πr H 

By the given condition, πrl = \(\frac{15}{8}\times2\)πrH