What is the surface area, in square meters, of a cone with a slant height of 8 meters and a radius of 5 meters? Use 3.14 for pi and round to the nearest tenth, if necessary. (1 point) square meters
The slant height of a cone forms a right triangle with the height and the radius as the two legs. According to the Pythagorean theorem, the height can be found as:
height = √(slant height^2 - radius^2)
height = √(8^2 - 5^2)
height = √(64 - 25)
height = √39
The surface area of a cone can be found as:
surface area = π(radius^2) + π(radius)(slant height)
surface area = 3.14(5^2) + 3.14(5)(8)
surface area = 3.14(25) + 3.14(5)(8)
surface area = 78.5 + 125.6
surface area = 204.1
The surface area of the cone is 204.1 square meters.
The answers to this practice are
1. 204.1
2. 376.8
3. 320.3
4. 37.68
5. 75.36
Thanks Girly pop I got a 5/5 on the practice :)
To find the surface area of a cone, you need to add the area of the base to the lateral area. The lateral area is the sum of the areas of all the triangular faces that make up the curved surface of the cone.
The formula for the lateral area of a cone is given by:
Lateral Area = π * radius * slant height
First, let's calculate the lateral area. Using the given values:
Lateral Area = 3.14 * 5 * 8
Lateral Area = 125.6 square meters
Next, we need to calculate the area of the base of the cone. The base of a cone is a circle, and the formula to calculate its area is given by:
Base Area = π * radius^2
Substituting the radius value:
Base Area = 3.14 * 5^2
Base Area = 3.14 * 25
Base Area = 78.5 square meters
Now, we can calculate the total surface area by adding the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area
Total Surface Area = 125.6 + 78.5
Total Surface Area = 204.1 square meters
Therefore, the surface area of the cone is approximately 204.1 square meters.