An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is $(\frac{1}{6})$ of the volume of the cone is unfilled but hemisphere is formed on the top. Find the volume of the ice-cream. (Take $π = 3.14$ )

$Cone with hemisphere on top$

Question

An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is

(\frac{1}{6})

of the volume of the cone is unfilled but hemisphere is formed on the top. Find the volume of the ice-cream. (Take

π = 3.14

)

$Cone with hemisphere on top$

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Accepted Answer

Step 1: Volume of the cone $= \frac{1}{3} 	imes \pi 	imes 9 	imes 12 = 36\pi$ cm$^3$
Step 2: Volume of ice-cream in the cone $= \frac{5}{6} 	imes 36 	imes \pi = 30\pi$ cm$^3$
Volume of ice-cream on top $= \frac{2}{3} 	imes 27 	imes \pi = 18\pi$ cm$^3$
Step 3: Total volume of the ice-cream $= (30\pi + 18\pi) = 48\pi$ cm$^3$
$= 48 	imes 3.14 = 150.72$ cm$^3$

Question

Solution