Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A solid right circular cylinder of radius 10 units and height 20 units is taken and melted. In which of these figures should it be reformed so that the figure has maximum total surface area?
Last updated May 30, 2026
Correct Answer:
Option A —
Cube
To determine which shape will have the maximum total surface area when reformed from the melted cylinder, we can look at the geometric properties of the shapes listed.
Step 1: Understand the cylinder of diameter 20 units
The original cylinder has a radius of 10 units. Since the diameter is twice the radius, a diameter of 20 units means the radius is exactly 10 units. This option describes the exact same cylinder we started with, meaning its surface area would not change at all.
Step 2: Understand the nature of a Sphere and Hemisphere
A sphere is unique because it is the most efficient three-dimensional shape possible. For a fixed amount of volume, a sphere will always have the absolute minimum total surface area of any shape. A hemisphere spreads the volume out slightly more and adds a flat base, giving it more surface area than a sphere, but it is still highly efficient and keeps a low surface area.
Step 3: Understand the nature of a Cube
Unlike round shapes, a cube has sharp corners, flat faces, and straight edges. Because it is boxy rather than rounded, it is far less efficient at packing volume. To hold the exact same amount of volume as a sphere or a cylinder, a cube must spread its material out much more, which naturally creates a significantly larger total surface area.
Among all the options provided, the cube requires the largest surface area to contain the same amount of melted material.
Correct Answer: (A) Cube
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
