Imagine you have two similar triangular pyramids. The volume of the smaller triangular pyramid is 343 cm³ and the volume of the larger one is 729 cm³. What is the scale factor of the smaller figure to the larger figure?(1 point) Responses 11:20 11:20 1:14 1:14 7:9 7:9 5:9
The volume of a triangular pyramid is directly proportional to the cube of the scale factor.
Let V1 be the volume of the smaller pyramid (343 cm³) and V2 be the volume of the larger pyramid (729 cm³).
(V1/V2) = (s₁/s₂)³
(343/729) = (s₁/s₂)³
(7/9) = (s₁/s₂)³
Taking the cube root of both sides:
∛(7/9) = s₁/s₂
7/9 = s₁/s₂
Therefore, the scale factor of the smaller figure to the larger figure is 7:9.