Question

the formula $a = pi r(r + l)$ can be used to find the surface area, $a$, of a cone and the formula $v=\frac{1}{3}pi r^{2}h$ can be used to find the volume, $v$, of a cone. part a which equation describes the slant height, $l$, of the cone in terms of its surface area, $a$, and the radius of its base, $r$? oa $l=\frac{a}{pi r}$ ob $l=\frac{a}{2pi r}$ oc $l=\frac{a}{pi r}-r$ od $l=\frac{a - pi r}{r}$

Explanation:

Step1: Start with surface - area formula

Given $A=\pi r(r + L)$.

Step2: Expand the right - hand side

$A=\pi r^{2}+\pi rL$.

Step3: Isolate the term with $L$

$A-\pi r^{2}=\pi rL$.

Step4: Solve for $L$

$L=\frac{A}{\pi r}-r$.

Answer:

C. $L = \frac{A}{\pi r}-r$