Question

When a cylindrical glass is stacked over a conical glass as shown, the rim of the cylindrical glass lies in level to the topmost point of the conical glass' neck. If the circular mouths of both the glasses are identical, how many conical glasses of juice can one cylindrical glass hold?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$\text{Volume of a cone}=\frac{1}{3}\pi \times (Radius{)}^2\times Height$

$\text{Volume of a cylinder}=\pi \times (Radius{)}^2\times Height$

Now, the circular openings of both the glasses are identical.

Hence, the radii of both the conical glass and the cylindrical galss are the same.

Also, when stacked above the conical glass, the rim of the cylindrical glass reaches the topmost point of the conical glass' neck.

Hence, the heights of both the glasses are identical as well.


Now,

The number of conical glasses of juice that a cylindrical glass can hold can be calculated as:

$Number=\frac{Volumeofcylindricalglass}{Volumeofconicalglass}$

$=\frac{\pi \times (Radius{)}^2\times Height}{\frac{1}{3}\pi \times (Radius{)}^2\times Height}$

As the radii and heights are the same for both glasses, we get:

$Number=\frac{\pi }{\frac{1}{3}\pi }=\frac{1}{\frac{1}{3}}=3$

Therefore, if both the radii and the heights are identical, a cylindrcial glass can hold 3 conical glasses of juice.