Respuesta :

Answer:

[tex]l=\frac{S-\pi r^{2}}{\pi r}[/tex]

Explanation:

The surface area of a cone is calculated using the formula:

[tex]S=πr^2+πrl[/tex]

We want to solve for l.

First, subtract πr² from both sides of the equation:

[tex]\begin{gathered} S-\pi r^2=\pi r^2-\pi r^2+\pi rl \\ S-\pi r^2=\pi rl \end{gathered}[/tex]

Next, divide both sides by πr:

[tex]\begin{gathered} \frac{S-\pi r^2}{\pi r}=\frac{\pi rl}{\pi r} \\ l=\frac{S-\pi r^{2}}{\pi r} \end{gathered}[/tex]

The equation solved for l is:

[tex]l=\frac{S-\pi r^{2}}{\pi r}[/tex]