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The radius of sphere A is one half that of sphere B. How do the circumference and volume of sphere B compare to sphere A?

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Answer: The circumference of B is 2 times of that of A and its volume is 8 times that of A.

Step-by-step explanation:

User Nikjohn
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Final answer:

The circumference of sphere B is twice that of sphere A due to the radius being double, while the volume of sphere B is eight times that of sphere A, since volume scales with the cube of the radius.

Step-by-step explanation:

The radius of sphere A is half that of sphere B which affects their circumference and volume. The formula for the volume of a sphere is ¶4³/3πr³, and the formula for the circumference of a sphere is 2πr. If we denote the radius of sphere A as 'r', the radius of sphere B would be '2r'. Consequently, the circumference of sphere B would be twice that of sphere A, as it's directly proportional to the radius. However, the volume calculation is more dramatic due to the cubic relationship with the radius. The volume of sphere B is 2³, or 8 times that of sphere A.

User LiraNuna
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