Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A spherical shell with inner radius 20 units and outer radius 30 units is molten and reformed into 100 identical cubes. What will be the side length of each cube?
Last updated May 30, 2026
Correct Answer:
Option D —
2.92 units
The correct answer is (D) 2.92 units.
Step-by-Step Explanation
To find the side length of the cubes, we need to calculate the volume of the material in the hollow spherical shell and then divide that volume equally among the 100 cubes.
Step 1: Find the volume of the spherical shell
The volume of a sphere is found by multiplying 4/3 by pi (approximately 3.14159) and then multiplying by the radius cubed (the radius multiplied by itself three times).
To find the volume of just the shell, we take the volume of the outer sphere and subtract the volume of the inner sphere.
The outer radius is 30, and 30 cubed (30 times 30 times 30) is 27,000.
The inner radius is 20, and 20 cubed (20 times 20 times 20) is 8,000.
The difference between them is 27,000 minus 8,000, which equals 19,000.
Now, we complete the volume calculation for the shell:
4/3 multiplied by pi multiplied by 19,000 is approximately 79,587.01 cubic units.
Step 2: Find the volume of a single cube
Since this total volume is melted down and reshaped into 100 identical cubes, we divide the total shell volume by 100:
79,587.01 divided by 100 equals approximately 795.87 cubic units per cube.
Step 3: Calculate the side length of the cube
The volume of a cube is equal to its side length cubed (side times side times side). To find the individual side length, we need to find the cube root of 795.87 (the number that, when multiplied by itself three times, equals 795.87).
The cube root of 795.87 is approximately 2.92 units.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
