FTCE Professional Education Practice Exam

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Prepare for the FTCE Professional Education Test. Study with comprehensive flashcards and engaging multiple choice questions, each crafted with hints and detailed explanations. Enhance your confidence for success!

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What formula is used to find the total surface area of a right cone?

3.14(r^2) + 3.14(r)(square root of r^2 + h^2)
1/3Bh
2(3.14)(rh) + 2(3.14)r^2
(3.14)(r^2)(h)

The correct answer is: 3.14(r^2) + 3.14(r)(square root of r^2 + h^2)

The formula used to find the total surface area of a right cone is given by the first choice: 3.14(r²) + 3.14(r)(√(r² + h²)). This formula comprises two parts: the base area and the lateral surface area. The base area, which is a circle, is calculated as the area of a circle formula: πr² where π is approximately 3.14. The second part of the formula, 3.14(r)(√(r² + h²)), represents the lateral surface area, which can be derived by considering the cone’s slant height. The slant height (l) can be calculated using the Pythagorean theorem, resulting in l = √(r² + h²). Thus, the total surface area combines these two components to provide a complete measure of the exterior surface area of the cone. The other options provided do not pertain to the total surface area of a right cone; rather, they either describe different geometric measurements or do not fit the context of surface area calculations.