if the surface area of a cube is increasing at a rate of 3⋅6cm2/sec, retaining ifs shape, then the rate of change of its volume (in cm3 / sec), when the length of a side of the cube is 10 cm, is

# if the surface area of a cube is increasing at a rate of $3\cdot 6{\mathrm{cm}}^{2}/\mathrm{sec}$, retaining ifs shape, then the rate of change of its volume (in $c{m}^{3}$ / sec), when the length of a side of the cube is , is

1. A

20

2. B

10

3. C

18

4. D

9

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Let the length an edge of the cube at any moment $t$

be  Then, its surface area $S$ and volume $V$ are given by

$S=6{x}^{2}$ and $V={x}^{3}$

and $\frac{dV}{dt}=3{x}^{2}\frac{dx}{dt}$

and $\frac{dV}{dt}=3×{10}^{2}×\frac{dx}{dt}$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)