Question

The formula for the surface area S of a cone is S = 2+ats 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 220 square feet and the radius is 7 feet. Approximate to the nearest tenth.

DEC

Answer 1

The formula for solving s in terms of the surface area and radius of a cone is s = (S - 2πr)/(πr). For a given surface area of 220 square feet and radius of 7 feet, the slant height is approximately 9.3 feet.

Step-by-step explanation:

To solve the formula for s, we need to isolate s on one side of the equation. The formula is given by:

`S = 2\pi r + \pi rs`

Step 1: Subtract 2πr from both sides of the equation to isolate the rs term:

`S - 2\pi r = \pi rs`

Step 2: Divide both sides of the equation by πr to solve for s:

`(S - 2\pi r)/(\pi r) = s`

Therefore, the formula for s is s =
`(S - 2\pi r)/(\pi r).`

To find the slant height when the surface area is 220 square feet and the radius is 7 feet, substitute the given values into the formula:

`s = (220 - 2\pi (7))/(\pi (7))`

Calculate the value of s using a calculator to obtain a value of approximately 9.3 feet.