Question

# A hemispherical bowl of internal diameter $$36\ cm$$ contains a liquid. This liquid is to be filled in cylindrical bottles of radius $$3\ cm$$ and height $$6\ cm$$. How many bottles are required to empty the bowl?

Solution

## We haveRadius of hemispherical bowl$$=\dfrac{36}{2}=18cm$$Volume of hemispherical bowl$$=\cfrac { 2 }{ 3 } \pi \times { (18) }^{ 3 }{ cm }^{ 3 }\left[ V=\cfrac { 2 }{ 3 } \pi { r }^{ 3 }\quad \right]$$Radius of a cylindrical bottle $$=3cm$$Height of a cylindrical bottle $$=6cm$$Volume of a cylindrical bottle $$=\left( \pi \times { 3 }^{ 2 }\times 6 \right) { cm }^{ 3 }$$   ....... $$v=\pi r^2 h$$Suppose $$x$$ bottles are required to empty the bowlVolume of $$x$$ cylindrical bottles $$=\left( \pi \times 9\times 6\times x \right) { cm }^{ 3 }$$Clearly volume of liquid in $$x$$ bottles = Volume of bowl$$\Rightarrow \pi \times 9\times 6\times x=\cfrac { 2 }{ 3 } \pi \times { (18) }^{ 3 }$$$$\Rightarrow x=72\quad$$$$\therefore$$ Bottles required to empty the bowl$$=72$$Mathematics

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