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Solid A is similar to solid B. If the volume of Solid A is 21 in3 and the volume of Solid B is 4,536 in3, how many times smaller is Solid A than Solid B?

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If Solid A is similar to Solid B, then their corresponding linear dimensions are proportional. The ratio of their volumes is the cube of the ratio of their linear dimensions.

Let's say the linear dimension of Solid A is x, and the linear dimension of Solid B is y. Then we can set up a proportion:

x/y = k (where k is the constant of proportionality)

If the volume of Solid A is 21 in^3, then:

x^3 = 21

Solving for x, we get:

x = cuberoot(21) ≈ 2.758

Similarly, if the volume of Solid B is 4,536 in^3, then:

y^3 = 4536

Solving for y, we get:

y = cuberoot(4536) ≈ 17.306

The ratio of their volumes is:

(21 in^3) / (4536 in^3) ≈ 0.00463

So Solid A is about 0.00463 times smaller than Solid B. Alternatively, we can say that Solid B is about 216 times larger than Solid A (the reciprocal of 0.00463).
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