#### Question

The side of a square sheet is increasing at the rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?

#### Solution

\[\text { Given }: A = x^2 \text { and } \frac{dx}{dt}= 4 cm/min \]

\[\text { Letxbe the side of the square andAbe its area at any timet.Then },\]

\[A = x^2 \]

\[ \Rightarrow \frac{dA}{dt} = 2x\frac{dx}{dt}\]

\[ \Rightarrow \frac{dA}{dt} = 2 \times 8 \times 4 \left[ \because x = 8 cm\text { and } \frac{dx}{dt} = 4 cm/\min \right]\]

\[ \Rightarrow \frac{dA}{dt} = 64 \ {cm}^2 /\min\]

Is there an error in this question or solution?

Solution The Side of a Square Sheet is Increasing at the Rate of 4 Cm per Minute. at What Rate is the Area Increasing When the Side is 8 Cm Long? Concept: Rate of Change of Bodies Or Quantities.