Final answer:
To find the surface area of a cone with a given slant height and base radius, calculate the base area using A = πr^2 and the lateral surface area using A = πrℓ, then add them together.
Step-by-step explanation:
To find the surface area of a cone, we need to find the area of the base and the lateral surface area. The base area can be calculated using the formula A = πr^2, where r is the base radius. The lateral surface area can be calculated using the formula A = πrℓ, where r is the base radius and ℓ is the slant height.
First, calculate the base area: A = π(2.60 cm)^2 = 21.237 cm^2 (rounded to the nearest 0.01 cm^2).
Next, calculate the lateral surface area: A = π(2.60 cm)(7.40 cm) = 60.846 cm^2 (rounded to the nearest 0.01 cm^2).
Finally, add the base area and the lateral surface area to find the total surface area: A = 21.237 cm^2 + 60.846 cm^2 = 82.083 cm^2 (rounded to the nearest 0.01 cm^2).