question_answer

The \[\frac{3}{4}th\] part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Answer:

According to the question,

\[\frac{3}{4}\] volume of water in conical vessel = Volume of cylindrical vessel

\[\frac{3}{4}\times \frac{1}{3}\times \pi \times {{r}^{2}}_{cone}\times {{h}_{cone}}=\pi {{r}^{2}}_{cy}{{h}_{cy}}\]

Or                     \[{{h}_{cy}}=\frac{1}{4}\times \frac{{{r}^{2}}_{cone}\times {{h}_{cone}}}{{{r}^{2}}_{cy}}\]

\[\Rightarrow \]               \[=\frac{1}{4}\times \frac{5\times 5\times 24}{10\times 10}=\frac{3}{2}\]

\[=1.5\,\,cm\]

Hence, height of water in cylindrical vessel is \[1.5\text{ }cm\].