Final answer:
Calculating the lateral surface area of a cone requires knowing either the radius and slant height or the radius and height. With only the volume provided and no additional dimensions, it's not possible to calculate the lateral surface area of the cone.
Step-by-step explanation:
The lateral surface area of a cone (A) can be determined using the formula A = πrl, where r is the radius of the base and l is the slant height of the cone. However, the question does not provide the necessary dimensions to calculate the lateral surface area directly. Instead, we are given the volume of the cone, which is 39 cm³.
To find the lateral surface area with the given volume, we first need to use the formula for the volume of a cone, which is V = (ρ5/3)r²h, where V is the volume, r is the radius, and h is the height. Solving for the radius or height with the given volume will require knowing one of these two dimensions, which the question does not provide.
Therefore, without additional information, we cannot determine the lateral surface area of this particular cone.