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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES2 Marks
Question
A balloon, which always remains spherical has a variables radius. Find the rate at which its volume is increasing with the radius when the later is $10 cm$.
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Answer

Since, v $=\frac{4}{3}{\pi \text{x}^3}$
$ \therefore \ \frac{\text{dV}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\Big(\frac{4}{3}{\pi}\text{x}^3 \Big) =\frac{4}{3}{\pi.}3\text{x}^2 = 4{\pi}\text{x}^2$
$ \Rightarrow \ \frac{\text{dV}}{\text{dx}}=4{\pi}(10)^2 =400{\pi}$
Therefore, the volume is increasing at the rate of $400p\ cm^3/\sec$.

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