Question

Question 9
An ice–cream cone full of ice cream having radius 5 cm and height 10 cm as shown I figure. Calculate the volume of ice- cream, provided that its $\frac{1}{6}$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 $=5cm$
$\therefore$ Volume of hemisphere -

$=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times (5{)}^3$
$=\frac{5500}{21}=261.90c{m}^3$
Now, radius of the cone$=5cm$
And height of the cone $=10–5=5cm$
$\therefore Volumeofthecone=\frac{1}{3}\times \frac{22}{7}\times (5{)}^2\times 5$
$=\frac{2750}{21}=130.95c{m}^3$
Now, total volume of ice – cream cone $=261.90+130.95=392.85c{m}^3$
Since $\frac{1}{6}$ part is left unfilled with ice – cream.
$\therefore$ Required volume of ice – cream-

$=392.85–392.85\times \frac{1}{6}=392.85-65.475$
$=327.4c{m}^3$