Question

A right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{be}r\mathrm{and}h,\mathrm{respectively}.\mathrm{Then}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}=r\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}=h \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{cones}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}}{\mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{cone}} \\ =\frac{\mathrm{\pi }{r}^{2}h}{\left({\displaystyle \frac{1}{3}}\mathrm{\pi }{r}^{2}h\right)} \\ =3 \end{gathered}$$

So, the number of cones that will be needed to store the water is 3.