Applications Of Derivatives Question 206
Question: The length of the side of a square sheet of metal is increasing at the rate of $ 4cm/\sec $ . The rate at which the area of the sheet is increasing when the length of its side is 2 cm, is
Options:
A) $ 16,cm^{2}/\sec $
B) $ 8,cm^{2}/\sec $
C) $ 32,cm^{2}/\sec $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given that rate of metal increasing $ =4cm/\sec =v=\frac{da}{dt} $
We know that area of square sheet =a2, (where a is side).
$ \therefore \frac{dA}{dt}=2a\frac{da}{dt}=2\times 2\times 4=16cm^{2}/\sec $ .
BETA
