A cylinder is filled to 4/5 th of its volume. It is, then tilted so that the level of water coincides with one edge of its bottom and top edge

Question

A cylinder is filled to \(\frac45\) th of its volume. It is, then tilted so that the level of water coincides with one edge of its bottom and top edge of the opposite side. In the process 30 cc of the water is spilled. What is the volume of the cylinder ?

Answer 1

Volume of the cylinder = πr²h. After tilting, by the given condition, cylinder is half full of water.

∴ \(\frac45πr^2h-30\frac12πr^2h\) ⇒ \(\big(\frac45-\frac12\big)πr^2h=30\)

⇒ \(\frac{3}{10}πr^2h=30\) ⇒ \(πr^2h=\frac{30\times10}{3}\) cc = 100 cc.