Question

The edge of a cube is decreasing at the rate of $0.04\, cm/sec$. If the edge of the cube is $10 \,cms$, then rate of decrease of surface area of the cube is...

• A. $4.8\, cm^2/sec$
• B. $4.08\, cm^2/sec$
• C. $48\, cm^2/sec$
• D. $4.008\, cm^2/sec$

Answer 1

Answer: (A)

Let edge of a cube be $x cm$, then surface area of the cube, $A=6 x^{2}$
It is given that, $\frac{d x}{d t}=-0.04 cm / sec$
Now, $\frac{d A}{d t} =12 x \frac{d x}{d t}$
$=12 x(-0.04) $
$=-0.48 x$
when, $x=10$, then$\frac{d A}{d t}=-0.48 \times 10$
$=-4.8 cm ^{2} / sec$