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