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Question 9
An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its 16part is left unfilled with ice – cream.

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Solution

Given, ice cream cone is the combination of a hemisphere and a cone.
Also, radius of hemisphere = 5 cm
Volume of hemisphere
=23πr3=23×227×(5)3=550021=261.90 cm3

Now, radius of the cone = 5 cm
And height of the cone = 10 – 5 = 5 cm
Volume of the cone=13×227×(r)2×h)Volume of the cone=13×227×(5)2×5=275021=130.95 cm3

Now, total volume of ice cream cone =Volume of the cone+Volume of hemisphere =261.90+130.95=392.85 cm3

Since 16 part is left unfilled with ice – cream.
Required volume of ice cream
=392.85 cm3(392.85×16) cm3=392.85 cm365.475 cm3=327.4 cm3


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