A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 20 meter per minute. How long would it take to fill a conical tank of radius 40 cm and depth 72cm?

Let the time taken by pipe to fill the tank is 't' minutes.

Rate of flow of water = 20 meter per minute

Length of water that flows through pipe in 't' minutes = 20t meters

= 20t(100) cm

= 2000t cm

Diameter of cylindrical pipe = 4 cm

Radius of cylindrical pipe,

Volume of water that flows through pipe in 't' minutes = πr²h

Where, r is radius of pipe and h is the length of water that flows through pipe in 't' minutes

⇒ Volume of water = π(2)²(2000t)

= 8000tπ cm³

Also, Volume of water that flows through pipe is equal to the volume of conical tank.

Radius of conical tank, r = 40 cm

Height of conical tank, h = 72 cm

Volume of conical tank , where r is radius of tank and h is the height(depth) of tank.

⇒ Volume of conical tank

Therefore, we have

8000tπ = 38400π

t = 4.8 minutes = 4 minutes 48 seconds.