What is the surface area in square meters of a cone with a slant height of 8 m and a radius of 5 m? Use 3.14 for pi and round to the nearest 10th if necessary.
First, calculate the slant height of the cone using the Pythagorean theorem:
l = sqrt(r^2 + h^2)
l = sqrt(5^2 + 8^2)
l = sqrt(25 + 64)
l = sqrt(89)
l ≈ 9.4 m
Next, calculate the lateral surface area of the cone:
A = πrl
A = 3.14 * 5 * 9.4
A ≈ 148.2 square meters
Finally, calculate the total surface area of the cone by adding the base area:
A = lateral surface area + base area
A = 148.2 + 3.14 * 5^2
A = 148.2 + 3.14 * 25
A = 148.2 + 78.5
A ≈ 226.7 square meters
Therefore, the surface area of the cone is approximately 226.7 square meters.