A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic meter per hour. Then the rate of increasing depth of wheat in tank is : (Take π = 3.14)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 m/h
The radius is fixed at 10 m, so the volume depends only on the depth h:
\( \displaystyle V=\pi(10)^{2}h=100\pi h \)
Differentiating with respect to time:
\( \displaystyle \frac{dV}{dt}=100\pi\frac{dh}{dt} \)
With \( \frac{dV}{dt}=314 \) and \( \pi=3.14 \):
\( \displaystyle \frac{dh}{dt}=\frac{314}{100\times 3.14} \)
\( \displaystyle =1\ \text{m/h} \)
NCERT (2026-27 edition):
Application of Derivatives
