Question

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Options

• 48 minutes 15 sec

• 51 minutes 12 sec

• 52 minutes 1 sec

•  55 minutes

Answer 1

The radius of cylindrical pipe

r = 5/2 mm = 0.25 cm

The volume per minute of water flow from the pipe

`=pi xx (0.25)^2 xx 1000`

`=62.5 pi cm^3`/minute`

The radius of cone

`=40/2`

`=20 cm`

Depth of cone = 24 cm

The volume of cone

`=1/3pi (20)^2 xx 24`

`= 3200 pi cm^3`

The time it will take to fill up a conical vessel

`=(3200pi)/(62.5pi)`

`=51 125/625 min`

`=51 min +125/625 xx 60 sec `

`=51 min + 12 sec`