Applications Of Derivatives Question 68
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
Options:
A) $ 432,cm^{3}/\sec $
B) $ 2160,cm^{3}/\sec $
C) $ 180,cm^{3}/\sec $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let velocity $ v=5,cm/\sec $ (Increasing the rate/sec is called the velocity) $ \frac{da}{dt}=5 $ …..(i) 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}} $
$ =2160cm^{3}/\sec $ ( $ \because $ edge $ a=12,cm) $ .
BETA
