A. πr(h + r) B. 2πrh C. πr2 + 2πrh D. πr2
Explanation:
The total surface area of a cone consists of two parts: the circular base and the lateral surface. The formula for the total surface area of a cone is: Total Surface Area = πr² + Lateral Surface Area where r is the radius of the circular base, and h is the height of the cone. The lateral surface area of a cone is given by the formula: Lateral Surface Area = πrℓ where ℓ is the slant height of the cone. To calculate the slant height, we can use the Pythagorean theorem: ℓ² = r² + h² Therefore, ℓ = √(r² + h²) Substituting this value for ℓ into the formula for the lateral surface area, we get: Lateral Surface Area = πr√(r² + h²) Combining this with the formula for the total surface area, we get: Total Surface Area = πr² + πr√(r² + h²) Simplifying this expression further, we get: Total Surface Area = πr² + 2πrh Therefore, the correct answer is option C (πr² + 2πrh).
