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Q.
If the diagonal of a square is changing at the rate of $0.5 \,cm\,s ^{-1}$. Then the rate of change of area, when the area is $400\, cm ^2$, is
Application of Derivatives
Solution:
$\text { Let square of side }= a $
$\therefore \text { diagonal }= a \sqrt{2} $
$\sqrt{2} \frac{ da }{ dt }=0.5 \text { and } a ^2=400 \Rightarrow a =20 $
$\therefore A = a ^2 \Rightarrow \frac{ dA }{ dt }=2 a \frac{ da }{ dt }$
$\frac{ dA }{ dt }=2 \times 20 \times \frac{1}{2 \sqrt{2}}=10 \sqrt{2} cm ^2 / s $