Question

using a rewritten 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 cone. use the formula to find the slant height, $l$, of a cone with a surface area of $1500\pi \text{ ft}^2$ and a radius of $15$ ft. $l = \square$ ft

Explanation:

Step1: Substitute given values

Substitute $S=1500\pi$ and $r=15$ into the formula:
$l = \frac{1500\pi - \pi(15)^2}{\pi(15)}$

Step2: Calculate $r^2$ and simplify terms

Compute $(15)^2=225$, then expand the numerator:
$l = \frac{1500\pi - 225\pi}{15\pi}$

Step3: Combine like terms in numerator

Subtract the terms in the numerator:
$l = \frac{1275\pi}{15\pi}$

Step4: Cancel $\pi$ and divide

Cancel $\pi$ from numerator and denominator, then divide:
$l = \frac{1275}{15} = 85$

Answer:

85 ft