Surface Area Of A Right Circular Cone

To find the number of vertices in a polyhedron with 4 faces and 6 edges, we use Euler's formula:

Euler's Formula: F + V - E = 2

Where:

Given:

Substituting the known values into Euler's formula:

4 + V - 6 = 2

Simplifying this equation:

V - 2 = 2

V = 4

Thus, the number of vertices is 4.

To find the curved surface area of a right circular cone, we first need to identify the values of the necessary dimensions. Given:

The formula for the curved surface area of a cone is:

CSA = πrl

where l is the slant height of the cone. We can calculate l using the Pythagorean theorem:

Substituting the given values:

Now substitute r and l into the curved surface area formula:

Therefore, the curved surface area of the cone is 65π cm².