Water flows at the rate of 10m/minute 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?
Water flows at the rate of 10m/minute 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 line to fill vessel = t minutes

Since water streams 10 m in 1 moment, it will stream 10t meters in t minutes.

As indicated by the inquiry,

Volume of funnel shaped vessel = Volume of water that goes through pipe in t minutes

Think about funnel shaped pope

Base Diameter = 40 cm

Base range, r = 20 cm

Tallness, h = 24 cm

We realize that the volume of cone = 1/3πr2h

Volume of cone shaped vessel \[=\text{ }1/3\pi \left( 20 \right)2\left( 24 \right)\text{ }=\text{ }3200\text{ }\pi \text{ }cm3\]

Think about barrel shaped line

Base width = 5 mm = 0.5 cm

Base span, r = 0.25 cm

Water covers 10t m distance in pipe,

Thus, we get,

Stature, h = 10t m = 1000t cm

We likewise realize that,

Volume of a chamber = πr2h

Volume of water passed in pipe \[=\text{ }\pi \left( 0.25 \right)2\left( 1000t \right)\text{ }=\text{ }62.5t\pi \text{ }cm3\]

In this way, we have

62.5tπ = 3200

62.5t = 3200

t = 51.2 minutes

We realize that,

0.2 minutes = 0.2(60) seconds = 12 seconds

Thusly, t = 51 minutes 12 seconds