Final answer:
The new volume of the triangular pyramid when the height is increased by a scale factor of 5 is 85 cm³.
Step-by-step explanation:
The question is asking for the new volume of a triangular pyramid when the height is increased by a scale factor of 5. To find the new volume, we use the fact that the volume of a pyramid is one third of the base area times the height (V = 1/3 * base area * height).
Because the scale factor only affects the height, we can calculate the new volume by simply multiplying the original volume by the scale factor. Hence, we multiple 17 cm³ (the original volume) by 5 (the scale factor for the height).
The new volume then is 85 cm³.