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)

Answer 1

To find the scale factor of the smaller figure to the larger figure, we need to calculate the ratio of their volumes.

Let x be the scale factor between the two figures.

Volume of smaller pyramid = x³ * Volume of larger pyramid

343 = x³ * 729

x³ = 343 / 729
x³ = 7 / 27
x = ∛(7 / 27)
x ≈ 0.629

Therefore, the scale factor of the smaller figure to the larger figure is approximately 0.629.

Answer 2

You got the rest of the answers?

Answer 3

I apologize for not providing the complete explanation in my previous response. Here is the complete solution:

Given:
Volume of smaller triangular pyramid = 343 cm³
Volume of larger triangular pyramid = 729 cm³

Let x be the scale factor from the smaller pyramid to the larger pyramid.

Since the volume of a pyramid is proportional to the cube of its dimensions, we can set up the following equation:

(x * side length of smaller pyramid)³ = side length of larger pyramid

(x * side length of smaller pyramid)³ = (side length of larger pyramid)³
x³ * (side length of smaller pyramid)³ = (side length of larger pyramid)³
x³ = (729 / 343)
x = ∛(729 / 343)
x = ∛(9 / 7)
x ≈ 1.15

Therefore, the scale factor of the smaller triangular pyramid to the larger triangular pyramid is approximately 1.15.