Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
Some metallic hemispheres of radius ‘R’ each, are taken. They are all melted together and moulded to make a sphere of radius 3R. How many hemispheres were there originally?
Last updated Jun 13, 2026
Correct Answer:
Option C —
54
To find the number of original hemispheres, we need to understand how the volume changes when the radius is tripled and how the shape changes from hemispheres to a full sphere.
Step 1: Understand the effect of tripling the radius
When you increase the radius of any three-dimensional object, its volume increases by the cube of that change. Since the new sphere has a radius that is 3 times larger than the original hemisphere's radius, its size factor increases by 3 times 3 times 3, which equals 27. This means a sphere with a radius of 3R has 27 times the volume of a sphere with a radius of R.
Step 2: Account for the difference between a hemisphere and a sphere
A hemisphere is exactly half of a full sphere. Therefore, it takes 2 hemispheres of the same radius to equal the volume of 1 full sphere of that same radius.
Step 3: Combine the factors to find the total number of hemispheres
To match the volume of a sphere with a radius that is 3 times larger, we need 27 times the volume of a standard sphere of radius R.
Since each hemisphere is only half of a standard sphere, we need twice as many hemispheres to make up that volume.
Multiplying 27 by 2 gives us 54.
Therefore, there were originally 54 hemispheres.
Correct Answer: (C) 54
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
