Final answer:
Tripling the dimensions of a cone will result in the surface area increasing by more than three times, because the base area and lateral surface area both depend on the square of the radius.
Step-by-step explanation:
To determine whether tripling the dimensions of a cone will triple the surface area, let's analyze the effect of scaling dimensions on surface area. The surface area of a cone consists of the base area (which is a circle) and the lateral surface area (the side).
For the base, the area is given by πr², where r is the radius of the base circle. When we triple the radius, the new area becomes π(3r)² = π9πr², which is 9 times the original area, not 3 times.
Similarly, the lateral surface area is also proportional to the square of the radius (because it includes the radius in its calculation), meaning that tripling the radius would also increase the lateral surface area by a factor of 9, not 3. Therefore, the surface area of the cone will increase by more than three times when the dimensions are tripled.
The correct answer to the question is: B. It will be more than triple the area because you square the radius to find the area of the base.