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(A) Let the side of the square be $a$ and its area be $A$.Given that the rate of change of the side length is $\frac{da}{dt} = 4 \, cm/sec$.The area o

Vedclass · Accepted Answer

$16$

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(A) Let the side of the square be $a$ and its area be $A$.Given that the rate of change of the side length is $\frac{da}{dt} = 4 \, cm/sec$.The area of the square is given by $A = a^2$.Differentiating both sides with respect to time $t$,we get:$\frac{dA}{dt} = \frac{d}{dt}(a^2) = 2a \frac{da}{dt}$.We need to find the rate of change of the area when $a = 2 \, cm$.Substituting the values $a = 2$ and $\frac{da}{dt} = 4$ into the equation:$\frac{dA}{dt} = 2 	imes 2 	imes 4 = 16 \, cm^2/sec$.Thus,the area of the sheet is increasing at the rate of $16 \, cm^2/sec$.

The length of the side of a square sheet of metal is increasing at the rate of $4 \, cm/sec$. The rate at which the area of the sheet is increasing when the length of its side is $2 \, cm$,is ........ $cm^2/sec$.

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