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

The Correct Option is A

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.