Question

Solve the formula for the indicated variable.surface area of cone; S=r^2+rl; solve for l.

Answer 1

Given:

The formula for the surface area of the cone is given as,

$\begin{gathered} S.A\text{ = }\pi r^2+\pi rl \\ \end{gathered}$

Required:

The modified formula for the surface area of the cone in terms of l.

Explanation:

The formula is given as,

$S=\pi r^2+\pi rl$

Taking common terms separately,

$\begin{gathered} S\text{ = }\pi r(r\text{ + l\rparen}_{\text{ }} \\ \end{gathered}$

Transposing the common terms to LHS,

$r\text{ + l = }\frac{S}{\pi r}$

Rearranging the equation for l,

$\begin{gathered} l\text{ = }\frac{S}{\pi r}\text{ - r} \\ l\text{ = }\frac{S-\pi r^2}{\pi r} \end{gathered}$

Answer:

Thus the required expression in terms of l is,

$l=\frac{\text{S-\pi r}^2\text{{}}}{\text{\pi r}}$