Question

the surface area of this cone is 785 square feet. what is the slant height of this cone? round your answer to the nearest hundredth. 10 ft s ≈ feet submit

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area formula of a cone is \(S=\pi r(r + s)\), where \(r\) is the radius and \(s\) is the slant height. Given \(S = 785\) square feet and \(r=10\) feet.

Step2: Substitute the known values into the formula

Substitute \(S = 785\), \(r = 10\) into \(S=\pi r(r + s)\). We get \(785=\pi\times10\times(10 + s)\).

Step3: Solve for \(s\)

First, simplify the equation: \(785 = 10\pi(10 + s)\). Then \(\frac{785}{10\pi}=10 + s\). Since \(\pi\approx3.14\), \(\frac{785}{10\times3.14}=10 + s\). Calculate \(\frac{785}{31.4}=10 + s\). \(25=10 + s\). Subtract 10 from both sides: \(s=25 - 10\).

Answer:

\(s = 15.00\) feet