Question

The base radius of a right circular cone is 3.5 cm and height is 12 cm. Find the slant height of the cone.

Hint:

The slant height of a right circular cone can be found using the Pythagorean theorem: \( l = \sqrt{r^2 + h^2} \).

Answer 1

We are given the base radius \( r = 3.5 \, \text{cm} \) and height \( h = 12 \, \text{cm} \). We need to find the slant height \( l \) of the cone. To find the slant height, we can use the Pythagorean theorem in the right triangle formed by the radius, height, and slant height: \[ l = \sqrt{r^2 + h^2}. \] Substituting the given values: \[ l = \sqrt{(3.5)^2 + 12^2} = \sqrt{12.25 + 144} = \sqrt{156.25}. \] Therefore, \[ l = 12.5 \, \text{cm}. \]
Conclusion: The slant height of the cone is \( 12.5 \, \text{cm} \).