JEE PYQ: Application Of Derivatives Question 32
Question 32 - 2020 (03 Sep Shift 2)
If the surface area of a cube is increasing at a rate of $3.6$ cm$^2$/sec, retaining its shape; then the rate of change of its volume (in cm$^3$/sec.), when the length of a side of the cube is 10 cm, is:
(1) $18$
(2) $10$
(3) $20$
(4) $9$
Show Answer
Answer: (4)
Solution
$S = 6a^2$, $\frac{dS}{dt} = 12a\frac{da}{dt} = 3.6 \Rightarrow \frac{da}{dt} = 0.03$. $\frac{dV}{dt} = 3a^2\frac{da}{dt} = 3(100)(0.03) = 9$.
BETA
