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 × 10⁻⁴ °C⁻¹).

Solution

Physics sir · 4 steps

Get the side from the surface area, then grow the volume with γ = 3α, not α.

1. Find the volume. A cube has 6 equal faces, so 6a² = 24 m² gives a² = 4 m² and a = 2 m. The volume is V = a³ = 8 m³.
2. Volume coefficient. Each of the three edges expands by the same fraction, so the volume coefficient is γ = 3α = 3 × 5.0 × 10⁻⁴ = 1.5 × 10⁻³ °C⁻¹.

   Δ V = Vγ Δ T = 8 × 1.5 × 10⁻³ × 10 = 0.12 m³

3. Convert units. 1 m³ = 10⁶ cm³, so 0.12 m³ = 1.2 × 10⁵ cm³.
4. So. The volume increases by 1.2 × 10⁵ cm³, which is option (b).

The idea to keep. Linear, area and volume coefficients go as α : β : γ = 1 : 2 : 3. Use the original size, multiply by the right coefficient and Δ T, and convert units only at the end.

Answer from the NTA final answer key. Solution by PrepWiser.