Geometry

Question Analysis
This question involves a real - world application of creating a cone from a semi - circular paper.
The main focus is on determining the radius and height of the cone formed based on the properties of the semi - circular paper and then calculating its volume using the cone volume formula.

Key Concept Explanation
When a semi - circular paper is rolled up to form a cone, the slant height of the cone is equal to the radius of the semi - circular paper.
The circumference of the base of the cone is equal to the arc length of the semi - circular paper.
The arc length of a semi - circle with radius is , and the circumference of a circle is (where is the radius of the circle), so , from which we can find the radius of the base of the cone.
Then, using the Pythagorean theorem (where is the height of the cone), we can find the height, and finally calculate the volume using .

Step - by - Step Solution
The radius of the semi - circular paper centimeters, so the slant height of the cone centimeters.
Since the arc length of the semi - circle is equal to the circumference of the base of the cone,