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)
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.
You got the rest of the answers?
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.