Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A solid cylinder made of aluminum is molten to form N identical right circular cones, such that radius of cone and cylinder are the same, and the height of cone is half of the height of a cylinder. What is the value of N?
Last updated May 30, 2026
Correct Answer:
Option B —
6
To find the value of N, we can look at how the volume of a single cone compares to the volume of the original cylinder based on their shapes and dimensions.
Step 1: Compare a cone and a cylinder with the exact same dimensions
If a cone and a cylinder have the exact same radius and the exact same height, the cone will always hold exactly one-third of the volume of the cylinder. In other words, it takes 3 identical cones to fill up 1 cylinder of the same size.
Step 2: Adjust for the difference in height
The problem states that the cones being made are not the same height as the cylinder; their height is only half the height of the cylinder. Since the height is cut in half, each of these shorter cones will have only half the volume of a full-height cone.
Step 3: Calculate the total number of cones
If the cones were full-height, we would get exactly 3 cones from the cylinder.
Because the cones are only half-height, each one takes up half as much space, meaning we can make twice as many of them from the same amount of aluminum.
Multiplying 3 by 2 gives us 6.
Therefore, the value of N is 6.
Correct Answer: (B) 6
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
