Question

what is the surface area of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 20 m 6 m 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 can see that the radius \( r = 6\space m \) and the slant height \( l=20\space m \), and \( \pi\approx3.14 \).

Step2: Calculate the lateral surface area

The lateral surface area (curved surface area) is \( \pi r l \). Substitute \( r = 6 \), \( l=20 \) and \( \pi\approx3.14 \) into the formula:
\( \pi r l=3.14\times6\times20 \)
First, calculate \( 6\times20 = 120 \), then \( 3.14\times120=376.8 \) square meters.

Step3: Calculate the base area

The base of the cone is a circle, and the area of a circle is \( \pi r^{2} \). Substitute \( r = 6 \) and \( \pi\approx3.14 \) into the formula:
\( \pi r^{2}=3.14\times6^{2} \)
First, calculate \( 6^{2}=36 \), then \( 3.14\times36 = 113.04 \) square meters.

Step4: Calculate the total surface area

Add the lateral surface area and the base area together:
\( S=376.8 + 113.04=489.84 \) square meters.

Answer:

\( 489.84 \)