Question

Each side of a square is increasing at a rate of 4 cm/s. at what rate is the area of the square increasing when the area of the square is 25 square centimeters?

Answer 1

The question is related to application of derivatives .

Let A represents the area and s represent the side length .

$A = s^2$

$25=s^2$

$s =\sqrt{25} = 5$

$A = s^2$

Differentiating both sides with respect to t

It is given that ds/dt = 4cm/s

Substituting the values of s, ds/dt and on multiplying them, we will get

dA/dt = 2(5)(4) = 40 cm^2/s

Therefore rate of change of area when area=$25 cm^2$ and rate of change of side is 4 cm/s is 40 $cm^2/s .$