Final answer:
The lateral surface area of a right circular cone with a 4-meter diameter and a 15-meter slant height is approximately 94.2 square meters.
Step-by-step explanation:
The lateral surface area of a right circular cone can be calculated using the formula L = πrl, where r is the radius of the cone's base and l is the slant height of the cone. Given that the diameter of the cone is 4 meters, the radius r is half of that, which is 2 meters. The slant height l is provided as 15 meters. Plugging these values into the formula gives us:
L = π * 2m * 15m = 30π m2
Using π approximately equal to 3.14159, we can calculate the lateral surface area of the cone to be approximately:
L ≈ 94.2 m2 (rounded to two significant figures, as the radius provided has two significant figures).