Question

find the surface area of the right cone given the radius and slant height shown. you can write your answer in terms of pi or round to the nearest hundreth. note that the figure is not to scale.

Explanation:

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

The surface area formula of a cone is \(S=\pi r(r + l)\), where \(r\) is the radius and \(l\) is the slant height.

Step2: Substitute the given values into the formula

Given \(r = 8\) and \(l=11\). Substitute into the formula: \(S=\pi\times8\times(8 + 11)\).

Step3: Simplify the expression

First, calculate \(8+11 = 19\). Then \(S=\pi\times8\times19=152\pi\). If we use \(\pi\approx3.14\), then \(S = 152\times3.14=477.28\).

Answer:

If in terms of \(\pi\), the surface area is \(152\pi\). If rounded to the nearest hundredth, the surface area is \(477.28\).