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Question
A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone if it is completely filled.
Solution
Diameter of the hemispherical bowl = 7.2 cm
Therefore, radius = 3.6 cm
Volume of sauce in hemispherical bowl = `2/3pir^3`
= `2/3pi xx (3.6)^3`
Radius of the cone = 4.8 cm
Volume of cone = `1/3pir^2h`
= `1/3pi xx (4.8)^2 xx h`
Now, volume of sauce in hemispherical bowl = volume of cone
`=> 2/3pi xx (3.6)^3 = 1/3pi xx (4.8)^2 xx h`
`=> h = (2 xx 3.6 xx 3.6 xx 3.6)/(4.8 xx 4.8)`
`=>` h = 4.05 cm
Height of the cone = 4.05 cm
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