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

#### 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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