This is one of the important question from the cbse board exam point of view because in 2004 and 2011 cbse board exam this question was asked. Question number 8 from RS Aggarwal book page number 810, exercise 17B, chapter volume and surface area of solid.

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# A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.

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Given data,

Inner diameter of the bowl = 30 cm

Inner radius of the bowl = 30/2 = 15 cm

Inner volume of the bowl = Volume of liquid

= [2/3] π r³

= [2/3] π 15³

= 7065 cm³

Radius of each bottle = 2.5 cm

Height = 6 cm

Volume of each bottle = πr²h

= π × [2.5]² ×6

= 117.75 cm³

Total number of bottles required = Volume of liquid / Volume of each bottle

= 7065 / 117.75

= 60

∴ Total number of bottles required are 60