Radius of Inscribed Sphere in Cone

Consider a right circular cone with a height of 12 cm and a base radius of 5 cm. A sphere is inscribed within the cone. Determine the radius of the inscribed sphere.

Use the formula for the radius of an inscribed sphere in a cone:

The radius $r$ of the inscribed sphere in a right circular cone can be given by:

$$ r = \frac{r_{b} h}{\sqrt{r_{b}^{2} + h^{2}} + r_{b}} $$

where:

• $r_{b}$ is the radius of the cone's base.
• $h$ is the height of the cone.