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...

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 cm2/sec (B) 4.08 cm2/sec (C) 48 cm2/sec (D) 4.008 cm2/sec

Tardigrade Admin · Accepted Answer

Let edge of a cube be x cm, then surface area of the cube, A=6 x2 It is given that, (d x/d t)=-0.04 cm / sec Now, (d A/d t) =12 x (d x/d t) =12 x(-0.04) =-0.48 x when, x=10, then(d A/d t)=-0.48 × 10 =-4.8 cm 2 / sec

Q. The edge of a cube is decreasing at the rate of $0.04 c m / sec$ . If the edge of the cube is $10 c m s$ , then rate of decrease of surface area of the cube is...

$4.8 c m^{2} / sec$

$4.08 c m^{2} / sec$

$48 c m^{2} / sec$

$4.008 c m^{2} / sec$

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

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

4.8cm2/sec

4.08cm2/sec

48cm2/sec

4.008cm2/sec