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When the dimensions of similar figures are multiplied by a scale factor of x, what is the volume multiplied by?

a) x
b) x²
c) x3
d) x^(−1)

User VOX
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1 Answer

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Final answer:

The volume of similar figures is multiplied by the cube of the scale factor, so when dimensions are multiplied by scale factor x, the volume multiplies by x^3.

Step-by-step explanation:

When the dimensions of similar figures are multiplied by a scale factor of x, the volume is multiplied by x3. Let's consider Block A with a volume of L x 2L x L = 2L3 and Block B with a volume of 2L x 2L x 2L = 8L3. Since Block B's dimensions are twice those of Block A (scale factor of 2), the volume is not just doubled but is in fact 8 times greater (23 = 8). This illustrates that volume scales with the cube of the scale factor.

User DisplayName
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