Question

The side of a square sheet is increasing at the rate of $4cm$ per minute. The rate by which the area increasing when the side is $8cm$ long is-

• A. $60c{m}^2/sec$
• B. $66c{m}^2/sec$
• C. $62c{m}^2/sec$
• D. $64c{m}^2/sec$

Answer 1

Answer: (D)

$64c{m}^2/sec$

Let the side of the square be $x$

given that $\frac{dx}{dt}=4$ $cm/\mathrm{minute}$

Now, $A=x^2$

$\Rightarrow \frac{dA}{dt}=2x\frac{dx}{dt}$

$\Rightarrow \frac{dA}{dt}=2x\times 4$

$\Rightarrow \frac{dA}{dt}=2\times 8\times 4$

$\Rightarrow \frac{dA}{dt}=64$ $c{m}^2/\mathrm{minute}$