Question

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is $50\%$ more than its height. If he diameter is same for both the bowl and the cylinder, then the amount of the beverage that can be poured from the bowl into the cylindrical vessel is __________.

• A. $66\frac{2}{3}\%$
• B. $78\frac{1}{2}\%$
• C. $100\%$
• D. None of these

Answer 1

The correct option is C $100\%$

We know that radius of both hemisphere and cylinder is same.

Let it be $r$

radius$\left(r\right)$ of cylinder is 50% more than its height$\left(h\right)$

$\therefore$ $r$ $=h+\frac{1}{2}h$

$⟹h=\frac{2}{3}r$

Now,

We know,

Volume of cylinder $=\pi r^{2}h$

$=\pi r^2\left(\frac{2}{3}r\right)=\frac{2}{3}\pi r^3$

Volume of hemisphere $=\frac{2}{3}\pi r^3$

$\because$ Volume of both cylinder and hemisphere are equal.

$\therefore$ $100\%$ liquid can be transfered.