(Originais Teachy 2023) - Question Medium of Mathematics

An architect is designing a new building and needs to calculate the amount of material needed to cover the surface of a water reservoir that will have the shape of a cone. The reservoir will be 10 meters high and the angle formed between the generatrix and the base of the cone is 60 degrees. To ensure waterproofing, he needs to determine the total surface area of the cone. Use the formula for the surface area of a cone, which is given by A = πr(r + l), where A is the surface area, r is the radius of the base, and l is the generatrix of the cone. To find the value of the radius, you can use the trigonometric relationship of the sine for the triangle formed by the generatrix, the radius of the base, and the provided angle. Consider π to be approximately 3.14 and do not forget that the generatrix of a cone is calculated through l = √(r^2 + h^2), where h is the height of the cone. After finding the surface area of the cone, calculate the amount of material in square meters that the architect will need to cover the reservoir.