Question

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are translated into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then how much beverage is contained in the vessel from the bowl?

• A. $66\frac{2}{3}$%
• B. $78\frac{1}{2}$%
• C. 100%
• D. More than 100 % (i.e., some liquid will be the left in the bowl)

Answer 1

The correct option is C 100%

Volume
of a hemisphere of radius 'r' $=\frac{2}{3}\pi r^3$
Since the diameter of the hemisphere and the cylinder are same, radius of the cylinder also $=r$
Given, $r=1.5\times height=\frac{3}{2}\times height$
$=>height=\frac{2}{3}r$
Volume
of a Cylinder of Radius "r" and height "h" $=\pi r^{2}h=\pi r^2\times \frac{2}{3}r=\frac{2}{3}\pi r^3$
Since, the volume of the hemisphere and the cylinder are equal, $100$ % of the beverage is contained in the vessel from the bowl.