An icecream cone full of icecream having radius 5 cm and height 10 cm as shown in fig. 16.77. Calculate the volume of icecream , provided that its 1/ 6 part is left unfilled with icecream .

#### Solution

Ice cream above the cup is in the form of a hemisphere

So, volume of the ice above the cup = \[\frac{2}{3} \pi r^3 = \frac{2}{3}\pi \left( 5 \right)^3 {cm}^3\]

Volume of the cup

\[\frac{1}{3}\pi \left( r \right)^2 h = \frac{1}{3}\pi \left( 5 \right)^2 \left( 5 \right) = \frac{1}{3}\pi \times 125\]

Now, 1/6 part of the total is left unfilled. So, 5/6 is filled.

So, the volume of ice cream

\[= \frac{5}{6}\left[\text { Volume of hemispherical cup + volume of cone }\right]\]

\[ = \frac{5}{6}\left[ \frac{2 \times 125\pi}{3} + \frac{125\pi}{3} \right]\]

\[ = \frac{5}{6} \times \frac{125\pi}{3}\left[ 2 + 1 \right]\]

\[ = 327 . 38 c m^3\]