The image shows a cone. The cone's base is a circle with a radius of 6 units, colored orange-gold. The cone itself is a pale yellow-beige color. A dashed line runs from the apex (point) of the cone to the center of the circular base. The slant height of the cone (the distance from the apex to a point on the edge of the base) is labeled as 11 unit. What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.s

Answer 1

To find the surface area of a cone, we need to calculate both the lateral surface area and the area of the circular base. The formula for the surface area \( S \) of a cone is given by:

\[ S = \pi r l + \pi r^2 \]

where:

• \( r \) is the radius of the base,
• \( l \) is the slant height of the cone.

From the information provided:

• The radius \( r = 6 \) units,
• The slant height \( l = 11 \) units,
• Using \( \pi \approx 3.14 \).

First, we calculate the lateral surface area:

\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 11 \]

Calculating this step-by-step:

1. Calculate \( 6 \times 11 = 66 \).
2. Then calculate \( 3.14 \times 66 = 207.24 \).

So the lateral surface area is \( 207.24 \) square units.

Next, we calculate the area of the circular base:

\[ \text{Area of Base} = \pi r^2 = 3.14 \times 6^2 \]

Calculating this:

1. Calculate \( 6^2 = 36 \).
2. Then calculate \( 3.14 \times 36 = 113.04 \).

So the area of the base is \( 113.04 \) square units.

Now, we can find the total surface area \( S \):

\[ S = \text{Lateral Surface Area} + \text{Area of Base} = 207.24 + 113.04 = 320.28 \]

Rounding to the nearest tenth, the total surface area of the cone is:

\[ \boxed{320.3} \text{ square units.} \]