Question

step by step bot answer this correcetly plzz 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 need to calculate the lateral surface area and then add it to the base area.

1. Start by finding the radius of the cone.
- The diameter is given as 12 feet, so the radius is half of that: 12 feet / 2 = 6 feet.

2. Next, calculate the lateral surface area.
- The lateral surface area of a cone is π times the radius times the slant height.
- Let's plug in the given values: π * 6 feet * 14 feet ≈ 263.89 square feet.
(Remember to use π ≈ 3.14 for the value of pi)

3. Now, calculate the base area.
- The base area of a cone is π times the radius squared.
- Let's calculate: π * (6 feet)^2 ≈ 113.04 square feet.

4. Finally, sum the lateral surface area and the base area.
- Add the values: 263.89 square feet + 113.04 square feet ≈ 376.93 square feet.

Therefore, the surface area of the cone is approximately 376.93 square feet.