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Question
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Solution
Height (h1) of cylindrical container = 15 cm
Radius (r1) of circular end of container = 12/2 =6 cm
Radius (r2) of circular end of ice-cream cone = 6/2 =3 cm
Height (h2) of conical part of ice-cream cone = 12 cm
Let n ice-cream cones be filled with ice-cream of the container.
Volume of ice-cream in cylinder = n × (Volume of 1 ice-cream cone + Volume of hemispherical shape on the top)
`pir_1^2h_1 = n(1/3pir_2^2h_2 + 2/3pir_2^3)`
`n = (6^2xx15)/(1/3xx9xx12+2/3xx(3)^3)`
`n = (36xx15xx3)/(108+54)`
n = 10
Therefore, 10 ice-cream cones can be filled with the ice-cream in the container.
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