Water flows at the rate of 10m min^-1 through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Let the time taken by pipe to fill vessel is t minutes

As water flows 10 m in 1 minute, it will flow 10t meters in t minutes.

Also,

Volume of conical vessel = Volume of water that passes through pipe in t minutes

Now, For conical pope

Base Diameter = 40 cm

Base radius, r = 20 cm

[as radius = diameter/2]

Height, h = 24 cm

We know that,

Where, r is base radius and h is the height of the cone.

Volume of conical vessel

For cylindrical pipe

Base diameter = 5 mm = 0.5 cm

[As 1 cm = 10 mm]

Base radius, r = 0.25 cm

[as radius = diameter/2]

Height, h = 10t m = 1000t cm

[∵ 1 m = 100cm]

[As water covers 10t m distance in pipe]

As we know,

Volume of a cylinder = πr²h

Where r is base radius and h is the height of cylinder

Volume of water passed in pipe = π(0.25)²(1000t) = 62.5tπ cm³

So, we have

62.5tπ = 3200

62.5t = 3200

t = 51.2 minutes

t = 51 minutes 12 seconds

[ as 0.2 minutes = 0.2(60) seconds = 12 seconds]