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Question
An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in the figure. Calculate the volume of ice cream, provided that its `1/6` part is left unfilled with ice cream.
Solution
Given, ice-cream cone is the combination of a hemisphere and a cone.
Also, radius of hemisphere = 5 cm
∴ Volume of hemisphere
= `2/3 pi"r"^3`
= `2/3 xx 22/7 xx (5)^3`
= `5500/21`
= 261.90 cm3
Now, radius of the cone = 5 cm
And height of the cone = 10 – 5 = 5 cm
∴ Volume of the cone
= `1/3 pi"r"^2"h"`
= `1/3 xx 22/7 xx (5)^2 xx 5`
= `2750/21`
= 130.95 cm3
Now, total volume of ice-cream cone
= 261.90 + 130.95
= 392.85 cm3
Since, `1/6` part is left unfilled with ice-cream.
∴ Required volume of ice-cream
= `392.85 - 392.85 xx 1/6`
= 392.85 – 65.475
= 327.4 cm3
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