Question

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 .

figure

Answer 1

Ice cream above the cup is in the form of a hemisphere
So, volume of the ice above the cup = $\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\mathrm{\pi }{\left(5\right)}^3{\mathrm{cm}}^3$
Volume of the cup = $\frac{1}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^2\mathrm{h}=\frac{{\displaystyle 1}}{{\displaystyle 3}}\mathrm{\pi }{\left(5\right)}^2\left(5\right)=\frac{{\displaystyle 1}}{{\displaystyle 3}}\mathrm{\pi }\times 125$
Now, 1/6 part of the total is left unfilled. So, 5/6 is filled.
So, the volume of ice cream
$$\begin{gathered} =\frac{5}{6}\left[Volumeofhemisphericalcup+volumeofcone\right] \\ =\frac{5}{6}\left[\frac{2\times 125\mathrm{\pi }}{3}+\frac{125\mathrm{\pi }}{3}\right] \\ =\frac{5}{6}\times \frac{125\mathrm{\pi }}{3}\left[2+1\right] \\ =327.38c{m}^3 \end{gathered}$$