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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)

Asked in JEE Main 25th June 2nd Shift 2022 · Areal and volume expansion

• (1) 2.4×10⁶ cm³
• (2) 1.2×10⁵ cm³
• (3) 6.0×10⁴ cm³
• (4) 4.8×10⁵ cm³

Step-by-step solution

Why the other options are wrong

• (1) comes from twenty times the answer, and no single step reaches it. The route worth checking is the six-faces slip, using 6α because a cube has six faces: 6α VΔ T=0.24 m³=2.4×10⁵ cm³, one decade below this option, with a stray m³→cm³ factor making up the rest. The 3 in γ=3α counts dimensions, not faces.
• (3) comes from reading a²=4 as the volume and using V=4 m³: 3α VΔ T=3(5×10⁻⁴)(4)(10)=0.06 m³=6.0×10⁴ cm³. The side is a=2 m and the volume is a³=8 m³.
• (4) comes from expanding the surface and then multiplying by a side: Δ A=2α AΔ T=2(5×10⁻⁴)(24)(10)=0.24 m², and 0.24× a=0.48 m³=4.8×10⁵ cm³. The areal coefficient 2α belongs to a surface; a volume needs 3α applied to V directly.

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