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.

Answer 1

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