This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the slant height (l) of the cone. The radius (r) is 6 cm and the height (h) is 8 cm. The slant height can be found using the Pythagorean theorem: l = sqrt(r^2 + h^2) l = sqrt(6^2 + 8^2) l = sqrt(36 + 64) l = sqrt(100) l = 10 cm Step 2: Calculate the surface area (A) of the cone. The formula for the surface area of a cone is the sum of the area of the base ( r^2) and the lateral surface area ( r l): A = r^2 + r l Substitute the values r = 6 cm and l = 10 cm into the formula: A = (6)^2 + (6)(10) A = 36 + 60 A = 96 cm^2 The surface area of the cone is 96 cm^2. Send me the next one 📸