Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A frustum has a top radius of 20 cm and bottom diameter of 60 cm. The height of this frustum is 40 cm. Now, a right circular cone is to be fitted over this frustum so that the structure formed is a right circular cone. What should be the height of the cone that is to be fitted?
Last updated Jun 13, 2026
Correct Answer:
Option B —
80 cm
To find the height of the cone that needs to be fitted on top, we can use the concept of proportional shapes and slopes.
Step 1: Standardize the measurements
First, let's look at the two circular faces of the frustum:
The bottom face has a diameter of 60 cm, which means its radius is half of that, or 30 cm.
The top face has a radius of 20 cm.
Step 2: Understand how the shape tapers
As we move up the frustum from the bottom to the top, the radius shrinks.
The radius goes from 30 cm down to 20 cm, which is a decrease of 10 cm.
This shrinking of 10 cm happens over the frustum's height of 40 cm.
This tells us the rate of tapering: for every 40 cm of height, the radius decreases by 10 cm.
Step 3: Calculate the height needed to complete the cone
To turn this frustum into a full, pointed cone, the top radius of 20 cm must continue to shrink at that exact same rate until it reaches a radius of 0 cm at the very peak.
We need the radius to decrease by another 20 cm (from 20 cm down to 0 cm).
Since a 10 cm decrease requires 40 cm of height, a 20 cm decrease (which is twice as much) will require twice as much height.
Multiplying 40 cm by 2 gives us 80 cm.
Therefore, the height of the cone to be fitted on top is 80 cm.
Correct Answer: (B) 80 cm
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
