The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ΔT so that its new temperature is T + ΔT. The increase in the volume of the sphere is approximately

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2πR∝ΔT

πR2αΔT

4πR3αΔT/3

4πR3αΔT

answer is D.

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Detailed Solution

Initial vol= 43πR3Final vol= 43π(R+R∆T)3=43πR3(1+∆T)3 =43πR3(1+3∆T) 43πR3+4πR3∆TThus increase in vol= 4πR3∆T

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