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A hemispherical bowl of radius 9 cm cont...

A hemispherical bowl of radius 9 cm contains a liquid. This liquid is to be filled into cylindrical small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl ?

A

`44`

B

`54`

C

`34`

D

`24`

Text Solution

Verified by Experts

The correct Answer is:
B
Radius of the hemispherical bolw, R = 9 cm.
Volume of liquid in the bowl `=2/3piR^(3)`
`=(2/3pixx9xx9xx9)cm^(3)`
`=(846 pi) cm^(3)`.
Radius of each cylindrical bottle, `r=3/2 cm`.
Height of each cylindrical bottle, `h = 4 cm`.
Volume of each cylindrical bolttle
`=pir^(2)h=(pixx3/2xx3/2xx4)cm^(3)=-(9pi)cm^(3)`
`"Required number of bolttles"=("volume of liquid in the bowl")/("volume of each bottle")=(486pi)/(9pi)=54`.
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