Question

A conical container is fully filled with petrol .the radius is 10 m and the height is 15m if the container can release the petrol through its bottom at the rate of 25 cute. meter per minute in how many minutes the container will be emptied round of your answer ​

Answer 1

Answer:

63  minutes.

Step-by-step explanation:

Volume of petrol

= 1/3 pi r^2 h

= 1/3 pi 100 15

= 1570.796 m^3

So time to empty = 1570.796 / 25

= 62.8319 minutes.

Answer 2

Answer:

The container will be emptied in 63 minutes.

Step-by-step-explanation:

We have given that,

For a conical container filled with petrol,

• Radius ( r ) = 10 m
• Height ( h ) = 15 m
• Rate of releasing petrol = 25 m³/min

We have to find the time required for the container to empty.

We know that,

$\displaystyle{\boxed{\pink{\sf\:Volume\:of\:cone\:=\:\dfrac{1}{3}\:\pi\:r^2\:h\:}}}$

$\displaystyle{\implies\sf\:Volume\:of\:container\:=\:\dfrac{1}{\cancel{3}}\:\times\:3.14\:\times\:(\:10\:)^2\:\times\:\cancel{15}}$

$\displaystyle{\implies\sf\:Volume\:of\:container\:=\:3.14\:\times\:100\:\times\:5}$

$\displaystyle{\implies\sf\:Volume\:of\:container\:=\:314\:\times\:5}$

$\displaystyle{\implies\:\boxed{\blue{\sf\:Volume\:of\:container\:=\:1570\:m^3\:}}}$

Now,

$\displaystyle{\boxed{\green{\sf\:Time\:required\:to\:empty\:container\:=\:\dfrac{Volume\:of\:container}{Rate\:of\:releasing\:petrol}}}}$

$\displaystyle{\implies\sf\:Time\:required\:to\:empty\:container\:=\:\dfrac{\cancel{1570}\:m^3}{\cancel{25}\:m^3\:/\:min}}$

$\displaystyle{\implies\sf\:Time\:required\:to\:empty\:container\:=\:\dfrac{\cancel{314}\:\cancel{m^3}}{\cancel{5}\:\dfrac{\cancel{m^3}}{min}}}$

$\displaystyle{\implies\sf\:Time\:required\:to\:empty\:container\:=\:\dfrac{62.8}{\dfrac{1}{min}}}$

$\displaystyle{\implies\sf\:Time\:required\:to\:empty\:container\:=\:62.8\:min}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:Time\:required\:to\:empty\:container\:\approx\:63\:min\:}}}}$

∴ The container will be emptied in 63 minutes.