Question

# Water flows at the rate of $$10$$ metre per minute through a cylindrical pipe having its diameter as $$5mm$$. How much time will it take to fill a conical vessel whose diameter of base is $$40cm$$ and depth $$24cm$$.

Solution

## we haveVolume of the water that flows out in one minuteVolume of the cylinder of diameter $$5mm$$ and length $$10$$ metreVolume of the cylinder of radius $$\left( \cfrac { 5 }{ 2 } mm =\cfrac { 1 }{ 4 } cm \right)$$ and length $$1000cm$$$$=\cfrac { 22 }{ 7 } \times \cfrac { 1 }{ 4 } \times \cfrac { 1 }{ 4 } \times 1000{ cm }^{ 3 }$$Volume of a conical vessel of base radius $$20cm$$ and depth $$24cm$$$$=\cfrac { 1 }{ 3 } \times \cfrac { 22 }{ 7 } \times { (20) }^{ 2 }\times 24{ cm }^{ 3 }\quad$$Suppose the conical vessel is filled in $$x$$ minutesVolume of the water that flows out in x minutes = Volume of the conical vessel$$\Rightarrow \cfrac { 22 }{ 7 } \times \cfrac { 1 }{ 4 } \times \cfrac { 1 }{ 4 } \times 1000\times x=\cfrac { 1 }{ 3 } \times \cfrac { 22 }{ 7 } \times { (20) }^{ 2 }\times 24$$$$\Rightarrow x=\cfrac { 512 }{ 10 } minutes\quad \quad \Rightarrow x=51\quad minutes\quad 12\quad seconds\quad$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More