Question

use the image to answer the question. what is the surface area of the cone? use 3.14 for pi and round to the nearest tenth, if necessary.

Explanation:

Step1: Calculate the base area

The formula for the area of a circle (base of the cone) is \(A_{base}=\pi r^{2}\). Given \(r = 6\) and \(\pi=3.14\), we have \(A_{base}=3.14\times6^{2}=3.14\times36 = 113.04\).

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cone is \(A_{lateral}=\pi rl\). Given \(r = 6\), \(l = 11\) and \(\pi=3.14\), we have \(A_{lateral}=3.14\times6\times11=3.14\times66 = 207.24\).

Step3: Calculate the total surface area

The total surface area of a cone \(A=A_{base}+A_{lateral}\). Substitute the values: \(A = 113.04+207.24=320.28\approx320.3\).

Answer:

\(320.3\)