Question
Two spheres are similar. The ratio of their radii is \( 2: 1 \). What is the ratio of their volumes? Please type your ariswer in the form of a ratio ( \( \mathrm{x}: \mathrm{y} \) ) with no spaces.
Ask by Sanders Mccarthy. in the United States
Mar 14,2025
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Answer
The ratio of their volumes is \(8:1\).
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The Deep Dive
The volume of a sphere is given by the formula \( V = \frac{4}{3} \pi r^3 \). If the ratio of their radii is \( 2: 1 \), then the volume of the larger sphere will be proportional to \( (2^3) \) while the smaller sphere will be proportional to \( (1^3) \). Calculating, we find that the ratio of their volumes is \( 2^3: 1^3 = 8: 1 \). So, the ratio of their volumes is \( 8:1 \).