Question

Water is being poured at the rate of 36 m$^3$/min into a cylindrical vessel whose circular base is of radius 3 meters. Then the water level in the cylinder increases at the rate of:

• A. \(\frac{4}{\pi} \, \text{m/min} \)
• B. \(4\pi \, \text{m/min} \)
• C. \(\frac{1}{4\pi} \, \text{m/min} \)
• D. \(\frac{\pi}{4} \, \text{m/min} \)

Hint:

For problems involving cylindrical shapes, remember to use the volume formula \(V = \pi r^2 h\) and differentiate with respect to time to find the rate of change of height.