Applications Of Derivatives Question 39
Question: If the edge of a cube increases at the rate of 60 cm per second, at what rate the volume is increasing when the edge is 90 cm
Options:
A) 486000 cu cm per sec
B) 1458000 cu cm per sec
C) 43740000 cu cm per sec
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{da}{dt}=60cm/sec, $ where a is edge and t is time. $ V=a^{3} $ .
$ \therefore \frac{dV}{dt}=3a^{2}\frac{da}{dt}=3a^{2}\times 60=180a^{2}=180\times {{(90)}^{2}} $
$ =1458000cm^{3}/sec $ .
BETA
