Question

what is the surface area of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 85 m 33 m cone diagram square meters submit

Explanation:

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

The surface area \( S \) of a cone is given by the sum of the lateral (or curved) surface area and the base area. The formula is \( S=\pi r l+\pi r^{2} \), where \( r \) is the radius of the base and \( l \) is the slant height of the cone.

From the diagram, we have \( r = 33\space m \) and \( l=85\space m \), and \( \pi\approx3.14 \).

Step2: Calculate the lateral surface area

The lateral surface area \( LSA=\pi r l \). Substitute \( r = 33 \), \( l = 85 \) and \( \pi=3.14 \):
\( LSA=3.14\times33\times85 \)
First, calculate \( 33\times85 = 2805 \)
Then, \( 3.14\times2805=8807.7 \)

Step3: Calculate the base area

The base of the cone is a circle, so the area of the base \( BA=\pi r^{2} \). Substitute \( r = 33 \) and \( \pi = 3.14 \):
\( BA=3.14\times33^{2} \)
First, calculate \( 33^{2}=1089 \)
Then, \( 3.14\times1089 = 3419.46 \)

Step4: Calculate the total surface area

The total surface area \( S=LSA + BA \)
Substitute the values of \( LSA \) and \( BA \) we found:
\( S=8807.7+3419.46=12227.16 \)

Answer:

\( 12227.16 \)