Question

The side of a square increases uniformly at rate of 1cm/sec. At what rate is the area increasing when the side of square is 6m.

Answer 1

Answer:

Explanation

Area = l^2

dA/dt = dl^2/dt

Or ....... 2l×dl/dt

Or..........2×6 ×0.01

dA/dt = 0.12 m^2/sec

Answer 2

Answer:

$0.12m^{2} /s$

Explanation:

Let side of square = L $m$

and Area of square be A $m^{2}$

Rate of increase of side of a square = $\frac{dL}{dT}$

                           $\frac{dL}{dT}$= $1cm/s=0.01m/s$

Rate of increase of Area of Square $=\frac{dA}{dT}$

                           $A = L^{2}$

                           $\frac{dA}{dT} = \frac{dL^{2} }{dT}$

                           $\frac{dA}{dT} = 2L\frac{dL}{dT}$

                           $\frac{dA}{dT} ( at L=6m) =2*6m*0.01m/s$

                           $\frac{dA}{dT} ( at L=6m) =0.12m^{2} /s$

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