Which of the following could represent the scale factor of the larger figure to the smaller figure? The larger triangle is v=343 in.3squared and tge smaller triangle is v=216 in. 3squared

Answer 1

To find the scale factor, we need to compare the corresponding lengths in both figures. Let's assume the larger triangle has side lengths a, b, and c, and the smaller triangle has side lengths x, y, and z.

Since the volume of a triangle is proportional to the cube of its side length, we can set up the following equation:

(a^3)/3 = 343
(x^3)/3 = 216

Simplifying and solving for a and x, we get:

a = 7 * (3)^(2/3)
x = 6 * (3)^(2/3)

Now we can compare the corresponding side lengths:

scale factor = (a/x) = (7/6)

Therefore, the scale factor of the larger figure to the smaller figure is 7/6.

Answer 2

Which of the following could represent the scale factor of the smaller figure to the larger figure if the smaller sphere is S.A = 20 pi yd 2squared and the larger one is S.A. = 125pi yd 2squared

Answer 3

To find the scale factor of the smaller figure to the larger figure, we need to compare the corresponding lengths in both figures. Let's assume the smaller sphere has a radius of r, and the larger sphere has a radius of R.

We know that the surface area of a sphere is proportional to the square of its radius, so we can set up the following equation:

4πr^2 = 20π
4πR^2 = 125π

Simplifying and solving for r and R, we get:

r = sqrt(5/π)
R = sqrt(125/4π) = 5/2 * sqrt(5/π)

Now we can compare the corresponding radii:

scale factor = (R/r) = (5/2 * sqrt(5/π)) / sqrt(5/π) = 5/2

Therefore, the scale factor of the smaller figure to the larger figure is 5/2.