Maths question from Social Forest Worker exam, 2026 by JKSSB
A right circular cylinder and a sphere have the same radius r. If their total surface areas are also exactly equal, what is the ratio of the volume of the cylinder to the volume of the sphere?
Last updated Jul 21, 2026
Correct Answer:
Option A —
3:4
Explanation
To find the ratio of their volumes, we first determine the height of the cylinder relative to its radius using their surface areas:
Equating Total Surface Areas:
The total surface area of a sphere is four multiplied by pi multiplied by the radius squared.
The total surface area of a cylinder is two multiplied by pi multiplied by the radius multiplied by the sum of its height and radius.
Setting these equal to each other and simplifying shows that the height of the cylinder must be equal to its radius.
Comparing Volumes:
The volume of the cylinder (with height equal to radius) is pi multiplied by the radius cubed.
The volume of the sphere is four-thirds multiplied by pi multiplied by the radius cubed.
Finding the Ratio:
Dividing the volume of the cylinder by the volume of the sphere gives one divided by four-thirds.
Simplifying this fraction yields three-fourths, which gives a volume ratio of 3:4.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
