Question

1. the formula for the surface area s of a cone is s = πr²+ πrs, where r is the radius and s is the slant height. solve the formula for s. justify each step. then find the slant height of the cone when the surface area is 113 square feet and the radius is 4 feet. approximate to the nearest tenth.

Explanation:

Step1: Isolate s in the surface - area formula

Given the surface - area formula of a cone $S=\pi r^{2}+\pi rs$. First, subtract $\pi r^{2}$ from both sides of the equation:
$S-\pi r^{2}=\pi rs$. Then, divide both sides by $\pi r$ to solve for s: $s = \frac{S-\pi r^{2}}{\pi r}$.

Step2: Substitute the given values

We are given that $S = 113$ square feet and $r = 4$ feet. Substitute these values into the formula for s:
First, calculate $\pi r^{2}=\pi\times4^{2}=16\pi\approx16\times3.14 = 50.24$.
Then, $S-\pi r^{2}=113 - 50.24=62.76$.
And $\pi r=3.14\times4 = 12.56$.
So, $s=\frac{62.76}{12.56}\approx5.0$.

Answer:

The slant height s is approximately 5.0 feet.