The side of a square sheet of metal is increasing at the rate of $3 \mathrm{~cm} / \mathrm{min}$. At what…

The side of a square sheet of metal is increasing at the rate of $3 \mathrm{~cm} / \mathrm{min}$. At what rate is the area increasing when the length of the side is $6 \mathrm{~cm}$ long?
  1. $36 \mathrm{~cm}^2 / \mathrm{min}$
  2. $12 \mathrm{~cm}^2 / \mathrm{min}$
  3. $18 \mathrm{~cm}^2 / \mathrm{min}$
  4. $9 \mathrm{~cm}^2 / \mathrm{min}$

Solution

$\mathrm{A}=\mathrm{a}^2$ and $\frac{\mathrm{da}}{\mathrm{dt}}=3 \mathrm{~cm} / \mathrm{min}$ Now $\frac{\mathrm{dA}}{\mathrm{dt}}=2 \mathrm{a} \frac{\mathrm{dA}}{\mathrm{dt}}$ $\Rightarrow \frac{\mathrm{dA}}{\mathrm{dt}}=2 \times 6 \times 3 \mathrm{~cm}^2 / \min =36 \mathrm{~cm}^2 / \min$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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