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The temperature of a metallic sphere of radius R is increased by a small amount Δ T. If the linear coefficient of thermal expansion of the metal is α, the approximate increase in the volume of the sphere is :

Asked in Re-NEET 2026 · Areal and volume expansion

• (1) 2π R³αΔ T
• (2) 3π R³αΔ T
• (3) 4π R³αΔ T
• (4) 6π R³αΔ T

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives this; it would mean a volume coefficient of 1.5α, while an isotropic solid has 3α.
• (2) No single slip gives this; it would mean a volume coefficient of 2.25α, while an isotropic solid has 3α.
• (4) No single slip gives this; it would mean a volume coefficient of 4.5α, while an isotropic solid has 3α.

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