PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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Solution for 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? - PUC Karnataka Science Class 12 - Mathematics

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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

\[\text { Given }: A = x^2 \text { and } \frac{dx}{dt}= 4 cm/min \]
\[\text { Letxbe the side of the square andAbe its area at any timet.Then },\]
\[A = x^2 \]
\[ \Rightarrow \frac{dA}{dt} = 2x\frac{dx}{dt}\]
\[ \Rightarrow \frac{dA}{dt} = 2 \times 8 \times 4 \left[ \because x = 8 cm\text { and } \frac{dx}{dt} = 4 cm/\min \right]\]
\[ \Rightarrow \frac{dA}{dt} = 64 \ {cm}^2 /\min\]

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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.
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