To find the surface area of a cone, we need to calculate the lateral surface area and the base area separately, and then add them together.
The lateral surface area of a cone is given by the formula: πrs, where r is the radius of the base of the cone and s is the slant height of the cone. The slant height can be calculated using the Pythagorean theorem: s = √(r^2 + h^2), where h is the height of the cone.
Given that the radius (r) is 2m and the height (h) is 6m, we can calculate the slant height s:
s = √(2^2 + 6^2) = √(4 + 36) = √40 ≈ 6.32 meters
Now we can calculate the lateral surface area of the cone:
Lateral surface area = π * 2 * 6.32 ≈ 39.83 square meters
The base area of a cone is πr^2, so the base area of this cone is:
Base area = π * 2^2 = 4π ≈ 12.57 square meters
Therefore, the total surface area of the cone is the sum of the lateral surface area and the base area:
Total surface area = 39.83 + 12.57 = 52.4 square meters
So, the surface area of the cone is approximately 52.4 square meters.
find the surface of the cone 6m 2m
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