If the side lengths of a cube are dilated from 10 yards to 31 yards, find the scale factor that relates the area of one face of the original cube to a face of the scaled cube. Write answer as number only, Round your answer to two decimal places if needed.

9.61

Step-by-step explanation:

The area of a face of the original cube is the square of its side length:

(10 yd) ² = 100 yd²

The area of a face of the dilated cube is the square of its side length:

(31 yd) ² = 961 yd²

Then the scale factor relating the area of the dilated cube to that of the original is ...

scale factor = (961 yd²) / (100 yd²)

scale factor = 9.61

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Perhaps you can see that this scale factor is (31/10) ², the square of the dilation factor.