Question

The edge of a cube is increasing at the rate of 5cm/sec.How fast is the volume of the cube increasing when the edge is 12cm long

• A. $432c{m}^3/sec$
• B. $2160c{m}^3/sec$
• C. $180c{m}^3/sec$
• D. $Noneofthese$

Answer 1

The correct option is B $2160c{m}^3/sec$

Let velocity v=5 cm/sec
(Increasing the rate/sec is called the velocity)
$\frac{da}{dt}=5....\left(i\right)$
Where a is distance and t is time.
But if a is edge of a cube, then $V=a^3$
Differentiating w.r.t. time t, so
$\frac{dV}{dt}=3a^2\frac{da}{dt}=3a^2.5=15a^2=15\times (12{)}^2$
$=2160c{m}^3/sec$ ($\because$ edge a =12 cm)