Question

the formula for the slant height of a cone is $l = \frac{s - \pi r^{2}}{\pi r}$, where $s$ is surface area of the the slant height, $l$, of a cone with a surface area of $1500\pi$ ft² and a radius of 15 ft. $l=square$ ft

Explanation:

Step1: Substitute values into formula

Given $S = 1500\pi$ and $r=15$. Substitute into $l=\frac{S - \pi r^{2}}{\pi r}$.
$l=\frac{1500\pi-\pi\times15^{2}}{\pi\times15}$

Step2: Simplify the numerator

First, calculate $\pi\times15^{2}=225\pi$. Then $1500\pi - 225\pi=1275\pi$. So $l=\frac{1275\pi}{15\pi}$.

Step3: Cancel out $\pi$ and divide

Cancel out $\pi$ in the numerator and denominator. Then $\frac{1275}{15}=85$.

Answer:

$85$