#### Please solve RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 21 maths textbook solution

$\pi ^{2}\: cm^{2}/sec$

Hint:

The circumference of a circle

$A(r)=\pi r^{2} \quad \quad \quad \quad \quad .....(i)$

Given:

$r=\pi \mathrm{cm} \\ \frac{2 d r}{d t}=1 \mathrm{~cm} / \mathrm{sec}$

Solution:

→ Differentiating (i) respect to t, we get

$\frac{d A}{d t}=2 \pi r \frac{d r}{d t}=\pi \times \pi \times 1 \\ \\ =\pi^{2} \mathrm{~cm}^{2} / \mathrm{sec}$
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