A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing w.r.t its radius when the radius is 1.1 cm. Give the answer in $c m^{2} .$

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answer is 15.2.

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Detailed Solution

Let the radius of balloon be $r, ∴ Volume = V = \frac{4}{3} π r^{3} .$

$∴$ Rate of change of volume with radius $\frac{d V}{d r} = \frac{d}{d r} (\frac{4}{3} π r^{3}) = \frac{4 π}{3} \frac{d}{d r} (r^{3}) = \frac{4 π}{3} .3 r^{2} = 4 π r^{2} .$

$∴ A t r = 1.1 c m, \frac{d V}{d r} = 4 π {(1.1)}^{2} = 15.2 c m^{2} .$

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