Question

Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 9 cm2

Answer 1

36 cm²s⁻¹ is the rate at which the area of the square is increasing.

Given each side of the square is increasing at a rate of 6cm/s

Area, A = s², s is the side length

=> $\frac{dA}{dt} =\frac{dA}{ds}* \frac{ds}{dt} =2s*(\frac{ds}{dt} )$ {chain rule of differentiation}

$\frac{ds}{dt}$ = 6 cm/s

When A = 9 cm² => 9 = s²

=> s = √(9) => s = 3 cm

Hence, $\frac{dA}{dt}$ = 2 × 3 × 6 = 36 cm²s⁻¹

Hence, 36 cm²s⁻¹ is the rate at which the area of the square increases

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