Question

A cylindrical tank of radius 10m is being filled with wheat at the rate of 314cubic mere per hour.Then the depth of the wheat is increasing at the rate of

• A. 1m/h
• B. 0.1m/h
• C. 1.1m/h
• D. 0.5m/h

Answer 1

Answer: (A)

1m/h

Answer 2

The correct answer is A:$1m/h$
Let $r$ be the radius of the cylinder. Then, volume $(V)$ of the cylinder is given by,
$V=π(radius)^2\times height$
$=π(10)^2h$
$=100πh$
Differentiating with respect to time $t$, we have:
$\frac{dV}{dt}=100π\frac{dh}{dt}$
The tank is being filled with wheat at the rate of 314cubic metres per hour.
$∴\frac{dV}{dt}=314m^3/h$
Thus, we have:
$314=100π\frac{dh}{dt}$
$⇒\frac{dh}{dt}=\frac{314}{100(3.14)}=\frac{314}{314}=1$
Hence, the depth of wheat is increasing at the rate of $1m/h.$
The correct answer is A.