A hollow sphere of radius R, a hollow cube of side R and a thin circular plate of radius R, made up of the same material, are all heated to 20°C above room temperature. When left to cool in the room, which of them will reach the room temperature first?

The cooling rate of a body in air is governed by Newton’s law of cooling: the rate of heat loss is proportional to the surface area exposed and the temperature difference with surroundings. Heat loss occurs via radiation and convection from the exposed surfaces [1]. For thin hollow objects of the same material and comparable thickness, the effective heat loss capability scales with exposed surface area. A hollow sphere of radius R has area 4πR^2, a thin circular plate (both faces) ≈2πR^2, and a cube of side R has area 6R^2; numerically 4πR^2 (≈12.57R^2) is largest. Therefore the sphere loses heat fastest and will reach room temperature first.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 7: Heat Transfer in Nature > 7.2.1 Land and Sea Breeze > p. 96
2. [2] Science-Class VII . NCERT(Revised ed 2025) > Chapter 7: Heat Transfer in Nature > In a Nutshell > p. 102