The surface area of a right circular cone with radius r and slant height l is which expression?

• A. SA = πr^2 + πrh
• B. SA = 2πr^2 + 2πrh
• C. SA = πr^2
• D. SA = πr^2 + πr√(r^2 + h^2)

Answer: (D)

Think about what makes up the surface area of a cone: the circular base and the curved lateral surface. The base contributes πr^2. The curved part has area equal to the base circumference times the slant height, which is πr times l. For a right circular cone, the slant height l relates to the vertical height h by l^2 = r^2 + h^2, so l = √(r^2 + h^2). Combine these parts: SA = πr^2 + πrl = πr^2 + πr√(r^2 + h^2). This matches the expression πr^2 + πr√(r^2 + h^2). The other options don’t fit because they replace l with h, double the surface area as if it were a cylinder, or give only the base area without the curved surface.