Given: the side of a square sheet is increasing at the rate of 4 cm per minute.

To find rate of area increasing when the side is 8 cm long

let the side of the given square sheet be x cm at any instant time.

Then according to the given criteria,

Rate of side of the sheet increasing is,

Then the area of the square sheet at any time t will be

A = x² cm².

Applying derivative with respect to time on both sides we get,

[from from equation(i)]

So when the side is 8cm long, the rate of area increasing will become

[from equation(ii)]

Hence the area is increasing at the rate of 64cm²/min when the side is 8 cm long