Question

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

Hint:

Use the Pythagorean theorem to find the slant height of a cone when you know the radius and height.

Answer 1

We are given the radius \( r = 3.5 \, \text{cm} \) and the height \( h = 12 \, \text{cm} \) of the cone. To find the slant height \( l \), we use the Pythagorean theorem, since the radius, height, and slant height form a right-angled triangle. The formula for the slant height is: \[ l = \sqrt{r^2 + h^2}. \] Substituting the values: \[ l = \sqrt{(3.5)^2 + (12)^2} = \sqrt{12.25 + 144} = \sqrt{156.25}. \] Thus, the slant height is: \[ l = 12.5 \, \text{cm}. \]
Conclusion: The slant height of the cone is \( 12.5 \, \text{cm} \).