Question

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temperature is T + ΔT. Calculate the increase in the volume of the metal box.

(1) 3a³αΔT 

(2) 4a³αΔT

(3) 4πa³αΔT

(4) \(\frac{4}{3}\pi a^3αΔT\)

Answer 1

(1) 3a³αΔT 

ΔV = V_γΔT
ΔV = 3a³αΔT 

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Answer 2

The Change in volume is given by the formula
ΔV=VγΔT 
The relationship between coefficient of volume expansion and coefficient of linear expansion is 
γ=3α
Hence the change in volume will be
ΔV=3a³αΔT