Chapter 12.7, Problem 26HP

To determine

To find:The slant height of a cone

Answer to Problem 26HP

The slant height of a cone is $l=\sqrt{r^2+h^2}$

Explanation of Solution

Calculation:

Consider the radius and height of a cone is known.

The objective is to describe the method to find the slant height of the cone.

Let l be the slant height of the cone, r be the radius of the cone and h be the height of the cone.

The slant height l, radius r and the height h from a right angle triangle as shown in the figure below.

  

Use Pythagorean Theorem

  $\begin{array}{l}{l}^2=r^2+h^2\\ l=\pm \sqrt{r^2+h^2}\end{array}$

Since height cannot be negative, so

  $l=\sqrt{r^2+h^2}$

Conclusion:Therefore, the slant height of the cone is $l=\sqrt{r^2+h^2}$ .