Question

Conical ice cream has a depth and radius of 6 inches and 1 inch respectively. If this ice cream is to be kept in a cylindrical vessel of the same radius and same height. Will the melted ice cream overflow the cylindrical vessel?

• A. Yes
• B. No

Answer 1

The correct option is B No

Let's draw the ice cream in the shape of a cone of a given depth and radius.
Given,
The radius of a conical ice cream $=r=1$ inch
The depth of a conical ice cream $=h=6$ inch

As we know,
The volume of a cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi \times 1^2\times 6$

$=\frac{\pi }{1}\times 2=2\pi$

Let's draw the cylindrical vessel of given depth and radius.
Given,
The Radius of a cylinder $=r=1$ inch
The depth of a cylinder $=h=6$ inch

As we know,
Volume of the cylinder $=\pi r^{2}h$
$=\pi \times 1^2\times 6=6\pi$

Concept:

• If the volume of a cone = volume of a cylinder, the cylindrical vessel will be filled with melted ice cream.
• If the volume of cone < volume of a cylinder, the cylindrical vessel will have some vacant space after filling with melted ice cream.
• If the volume of cone > volume of a cylinder, melted ice cream will overflow the cylindrical vessel.

The volume of a cone is less than the volume of a cylinder. Hence, the cylindrical vessels will have some vacant space after filling with melted ice cream.
Option (b) is correct.