A metallic sphere (the coefficient of linear expansion $α = 2 x 10^{- 6} / {}^{0}C$ ) of radius 10 cm is heated at the rate of 2°C per second. Its volume will increase at the rate of :

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$8 π \times 10^{- 3} {cm}^{3} / s$

6 x 10^-6 cm³/s

$16 π \times 10^{- 3} {cm}^{3} / s$

12 x 10^-6 cm³ /s

answer is C.

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Detailed Solution

$V = \frac{4}{3} {πr}^{3} \Rightarrow \frac{∆ V}{∆ t} = \frac{4 {πr}^{2} ∆ r}{∆ t} = (4 {πr}^{3}) (\frac{∆ r}{r ∆ t}) = (4 {πr}^{3}) (α \frac{∆ T}{∆ t}) = 16 π \times 10^{- 3} {cm}^{3} / s .$

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