Question

The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

Answer 1

The area of a square:

$S=a^2$

where a is side of a square.

$\frac{dS}{dt}=2a\frac{da}{dt}$

$a=\sqrt{S}=\sqrt{150}=5\sqrt{6}$ cm

$\frac{da}{dt}=10$ cm/s

$\frac{dS}{dt}=2\cdot 5\sqrt{6}\cdot 10=100\sqrt{6}$ cm²/s