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

Answer 1

Answer: (D)

$A=x^2,\frac{dx}{dt}=4cm/\min$
$\frac{dA}{dt}=2x\frac{dx}{dt}=8x$
$\Rightarrow$ at $x=8cm$
$\frac{dA}{dt}=64c{m}^2/\min$.