A solid metallic cube having total surface area 24 m 2 is uniformly heated. If its temperature is increased by 10 ° C , calculate the increase in volume of the cube. (Given α = 5 . 0 × 10 - 4 C ∘ - 1 ).

Step-by-step solution

Total surface area of a cube is 6 a 2 = 24   m 2 ⇒ a 2 = 4 ⇒ a = 2   m Volume of a cube V = a 3 = 8   m 3 Change in volume is given by, Δ V = V 0 γ Δ T , where γ = 3 α Δ V = 8 × 1 . 5 × 10 - 4 × 10   m 3 ⇒ Δ V = 1 . 2 × 10 5   cm 3