A cone has the height of 22cm and a diameter of 25cm. What is the surface area of the cone? Use 3.14 for pi. (1 point) Responses 1,354.125 square centimeters 1,354.125 square centimeters 863.5 square centimeters 863.5 square centimeters 2,383.26 square centimeters 2,383.26 square centimeters 3,689.5 square centimeters
To find the surface area of a cone, you need to calculate the lateral surface area and the base area, and then add them together.
The lateral surface area of a cone can be found using the formula:
Lateral Surface Area = π * radius * slant height
First, let's find the radius. The diameter is given as 25cm, so the radius is half of that:
Radius = 25cm / 2 = 12.5cm
Next, we need to find the slant height. We can use the Pythagorean theorem:
Slant height^2 = (Height^2) + (Radius^2)
Slant height^2 = (22cm)^2 + (12.5cm)^2
Slant height^2 = 484cm^2 + 156.25cm^2
Slant height^2 = 640.25cm^2
Slant height ≈ √640.25cm^2 ≈ 25.33cm
Now we can calculate the lateral surface area:
Lateral Surface Area = π * 12.5cm * 25.33cm
Lateral Surface Area ≈ 989.45cm^2
The base area of a cone can be found using the formula:
Base Area = π * radius^2
Now we can calculate the base area:
Base Area = π * (12.5cm)^2
Base Area ≈ 490.87cm^2
Finally, we can find the surface area by adding the lateral surface area and the base area:
Surface Area ≈ Lateral Surface Area + Base Area
Surface Area ≈ 989.45cm^2 + 490.87cm^2
Surface Area ≈ 1480.32cm^2
So the surface area of the cone is approximately 1480.32 square centimeters, which rounds to 1,480.32 square centimeters.