HELP NEEDED PLEASE! The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure. S. A. = 135 S. A. = 200 V = ? V = 300

V = 166.4

Step-by-step explanation:

The ratio of lengths of similar figures is the scale factor.

The ratio of the surface areas of similar figures is the square of the scale factor.

The ratio of the volumes of similar figures is the cube of the scale factor.

We don't know the scale factor of the figures, but we know the ratio of the surface areas is 200/135.

That is the square of the scale factor.

Let k = scale factor.

k² = 200/135 = 40/27

The ratio of the volumes is

k³ = [√(k²)]³

k³ = [√(40/27)]³ = 1.80320

V = 300/1.80320

V = 166.4

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