Question

Water flows at the rate of 20 metre/minute through a cylindrical pipe whose radius is 1.5 cm. Using this pipe, how long (in hours) would it take to fill a conical vessel whose radius is 120 cm and depth is 72 cm?

• A. 1.24
• B. 1.28
• C. 1.4
• D. 1.6

Hint:

Always convert units appropriately when working with volumes and rates, and use the formula for the volume of a cylinder and cone to calculate the time taken to fill a container.

Answer 1

The Correct Option is A

The volume of water flowing per minute is the volume of the cylinder, given by \( V = \pi r^2 h \), where \( r = 1.5 \) cm and \( h = 20 \) m = 2000 cm. The volume of the conical vessel is given by \( V = \frac{1}{3} \pi r^2 h \), where \( r = 120 \) cm and \( h = 72 \) cm.
Calculate the time taken to fill the conical vessel using the volume of water flowing per minute.