Maths question from Laboratory Attendant exam, 2026 by JKSSB
A right circular cone of largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?
Last updated Jun 19, 2026
Correct Answer:
Option B —
50%
Imagine a solid wooden hemisphere, which looks like a bowl turned upside down.
To carve out the largest possible cone from this hemisphere, the circular base of the cone must perfectly match the flat bottom of the hemisphere. At the same time, the pointed tip of the cone must reach the exact top center of the hemisphere's curved surface.
Because of this setup:
The width of the cone matches the width of the hemisphere.
The height of the cone matches the height of the hemisphere.
According to the laws of geometry, a hemisphere of a certain height and width holds a specific amount of space. A cone with those exact same dimensions holds exactly half of that space.
Since the cone takes up exactly half of the original hemisphere's volume, the remaining wood left over after carving it out must also be exactly half.
Expressed as a percentage, half of the original material is fifty percent.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
