Question

The side of a square sheet is increasing at rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?

Answer 1

Let a be the side of the square sheet.

A be the area

t be the time taken

Given $\frac{da}{dt}=4$

we know, $A=a^2$

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

$=\mathrm{2.8.4}$

$=64c{m}^2$ per min.