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 7:9 7:9 1:14 1:14 5:9 5:9
To find the scale factor between the two similar triangular pyramids, we need to compare their volumes.
Let the scale factor be x.
Since the volume of the smaller pyramid is 343 cm³ and the volume of the larger pyramid is 729 cm³, we can set up the proportion:
(343 * x³) / (729) = 1
Multiplying both sides by 729:
343 * x³ = 729
Divide by 343:
x³ = 729 / 343
x³ = 2.1266
Taking the cube root of both sides:
x ≈ 1.2926
Therefore, the scale factor of the smaller figure to the larger figure is approximately 1.2926.