A solid metallic cube having total surface area 24   m 2 is uniformly heated. If its temperature is…

A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube. (Given α=5.0×10-4C∘-1).
  1. 2.4×106 cm3
  2. 1.2×105 cm3
  3. 6×104 cm3
  4. 4.8×105 cm3

Solution

Total surface area of a cube is 6a2=24 m2⇒a2=4 ⇒a=2 m

Volume of a cube V=a3=8 m3

Change in volume is given by, 

ΔV=V0γΔT, where γ=3α

ΔV=8×1.5×10-4×10 m3⇒ΔV=1.2×105 cm3

Asked in: JEE Main 2022 (25 Jun Shift 2)

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