An ice-ceram cone full of ice-cream having radius 5 cm height 10 cm as shown if figure.

Calculate the volume of ice-cream, provided that its `(1)/(6)` part is left unfilled with ice-cream.

Answer

`= 327.4 cm^(3)`

Explanation

Given , ice - cream cone is the combination of a hemisphere and a cone.
Also, radius of hemisphere = 5 cm
`therefore` Volume of hemisphere `= (2)/(3) pir^(3) = (2)/(3) xx (22)/(7) xx (5)^(3)`
`= (5500)/(21) = 261.90 cm^(3)`
Now, radius of the cone = 5 cm
and heigth of the cone = 10-5 = cm
`therefore` Volume of the cone `= (1)/(3) pir^(2)h`
`= (1)/(3) xx (22)/(7) xx (5)^(2) xx 5`
`= (2750)/(21) = 130.95 cm^(3)`
Now, total volume of ice- cream cone` = 261.90+130.95= 392.85 cm^(3)`
Since,`(1)/(6)` parts is left unfilled with ice- cream.
`therefore` Required volume of ice - cream ` = 392.85-392.85 xx (1)/(6) = 392.85 - 64.475`
`= 327.4 cm^(3)`