Question

Surface area of a cone: S = πr² + πrl;solve for l.

Answer 1

`l=(S-\pi r^(2))/(\pi r)`

Explanation:

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

`S=πr^2+πrl`

We want to solve for l.

First, subtract πr² from both sides of the equation:

`\begin{gathered} S-\pi r^2=\pi r^2-\pi r^2+\pi rl \\ S-\pi r^2=\pi rl \end{gathered}`

Next, divide both sides by πr:

`\begin{gathered} (S-\pi r^2)/(\pi r)=(\pi rl)/(\pi r) \\ l=(S-\pi r^(2))/(\pi r) \end{gathered}`

The equation solved for l is:

`l=(S-\pi r^(2))/(\pi r)`