Question

Water flows at a rate of 10m per minute through a cylindrical pipe having its diameter as 20 mm. How much time will it take to fill a conical vessel of base diameter 40cm and depth 24cm.

Answer 1

hope this will help you

Answer 2

Given that,

Water flow at a rate = 10 m/ min

Diameter of cylindrical = 20 mm

Diameter of conical vessel = 40 cm

Depth = 24 cm

We need to calculate the amount of water required to fill the conical vessel

Using formula of volume of conical vessel

$V=\dfrac{1}{3}\pi\times r^2\times h$

Put the value into the formula

$V=\dfrac{1}{3}\times\pi\times(20)^2\times24$

$V=3200\pi$

We need to calculate the amount of water that flows out of cylindrical

Using formula of volume

$\volume\ flow\ in\ 1 min=\pi\times r^2\times h$

Put the value into the formula

$Volume = \pi\times(\dfrac{20}{20})^2\times10\times100$

$Volume= 1000\pi\ cm^3$

We need to calculate the required time to fill the vessel

Using formula of time

$t=\dfrac{volume\ of\ conical\ vessel}{Volume\ of\ water\ in\ 1\ min}$

Put the value into the formula

$t=\dfrac{3200\pi}{ 100\pi\times1}$

$t=3.2\ min$

Hence, The required time to fill the vessel is 3.2 min.