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.
1 answer:
Answer:
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.
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