Surface Area of Cones Practice

Question

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Question
What is the surface area, in square centimeters, of a cone with a diameter of 12 feet and a slant height of 14 feet? Use 3.14 for pi and round to the nearest tenth, if necessary.

Answer 1

To find the surface area of a cone, you can use the formula:

\[ \text{Surface Area} = \pi r^2 + \pi r l \]

where:

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

Step 1: Find the radius

The diameter of the cone is 12 feet, so the radius \( r \) is half of the diameter:

\[ r = \frac{12}{2} = 6 \text{ feet} \]

Step 2: Plug in the values into the formula

Given \( r = 6 \) feet and \( l = 14 \) feet, we can calculate the surface area:

1. Calculate the base area: \[ \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ square feet} \]

2. Calculate the lateral surface area: \[ \pi r l = 3.14 \times 6 \times 14 \] First, calculate \( 6 \times 14 \): \[ 6 \times 14 = 84 \] Now calculate the lateral surface area: \[ \pi r l = 3.14 \times 84 = 263.76 \text{ square feet} \]

Step 3: Add both areas

Now, add the base area and the lateral surface area to find the total surface area:

\[ \text{Surface Area} = 113.04 + 263.76 = 376.8 \text{ square feet} \]

Final Answer

Thus, the surface area of the cone is approximately 376.8 square feet.