Water flows out through a pipe, whose internal radius is 3 cm, at the rate of x cm per second into a cylindrical tank, the radius of whose base is 60 cm. If the level of water in the tank rises by 15 cm in 5 minutes, then the value of x is:

Correct option is B

​$$\textbf{Given:} \\\text{Internal radius of pipe} = 3 \text{ cm} \\\text{Speed of water flow} = x \text{ cm/s} \\\text{Radius of cylindrical tank} = 60 \text{ cm} \\\text{Rise in water level} = 15 \text{ cm} \\\text{Time} = 5 \text{ minutes} = 300 \text{ seconds} \\\textbf{Concept Used:} \\\text{Volume of water flowing per second equals volume increase in tank} \\\textbf{Formula Used:} \\\text{Volume of water per second through pipe} = \pi r^2 \times \text{speed} \\\text{Volume of cylinder} = \pi R^2 h \\\textbf{Solution:} \\\text{Volume of water flowing per second from pipe} \\= \pi \times 3^2 \times x \\= 9\pi x \\\text{Volume of water flowing in 300 seconds} \\= 9\pi x \times 300 \\= 2700\pi x \\\text{Increase in volume of water in tank} \\= \pi \times 60^2 \times 15 \\= \pi \times 3600 \times 15 \\= 54000\pi \\\text{Equating volumes:} \\2700\pi x = 54000\pi \\2700x = 54000 \\x = \frac{54000}{2700} \\x = 20 \\\textbf{Final Answer:} \\20$$​​