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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 have
Volume of the water that flows out in one minute

Volume of the cylinder of diameter $$5mm$$ and length $$10$$ metre

Volume 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 $$x$$ minutes

Volume 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

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