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The surface areas of two similar figures are 16 in² and 25 in². If the volume of the larger figure is 500 in³, what is the volume of the smaller figure?

A. 205 in³
B. 256 in³
C. 320 in³
D. 400 in³

Answer :

Final answer:

The volume of the larger figure is 500 in³.

Explanation:

To find the ratio of the volume of the larger figure to the smaller figure, we need to compare their surface areas. Let's assume the surface area of the smaller figure is 16 in², and the surface area of the larger figure is 25 in². The ratio of their surface areas is 25/16. Since the volume ratio is the cube of the surface area ratio, we can cube the ratio 25/16 to find the volume ratio. (25/16)³ = 125/64. So, the volume of the larger figure is 125/64 times the volume of the smaller figure. If the volume of the smaller figure is x, then the volume of the larger figure would be (125/64)x. We know that (125/64)x = 500. Solving for x, we get x = 256. Therefore, the volume of the smaller figure is 256 in³. To find the volume of the larger figure, we can substitute the value of x back into the equation: (125/64) * 256 = 500. Therefore, the volume of the larger figure is 500 in³.

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