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A cylindrical vessel of height 24cm and diameter 40cm is full of water. ____ is the exact number of small cylindrical bottles, each of height 10cm and diameter 8cm , which can be filled with this water.

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Detailed Solution

Now, the cylindrical vessel's height =24 cm,
diameter =40 cm radius =20 cm Volume V=

π r^{2} h

π 20^{2} . 24

small cylindrical bottles's height =10 cm diameter =8 cm, radius =4 cm
Volume V=

π 4^{2} 10

exact number of small cylindrical bottles = Volume cylindrical vessel /Volume of small cylindrical bottles
N=

\frac{π . 20^{2} . 24}{π . 4^{2} . 10}

On simplification
N = 60
60 is the exact number of small cylindrical bottles, each of height 10cm and diameter 8cm , which can be filled with this water.

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