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.

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UpStudy AI · Accepted Answer

1. The volume $$ V $$ of a sphere is given by the formula  
   $$
   V = \frac{4}{3}\pi r^3
   $$

2. Given the ratio of the radii is $$ 2:1 $$, let the radii be $$ 2r $$ and $$ r $$.

3. The volumes of the spheres are proportional to the cube of their radii. Thus, the ratio of the volumes is  
   $$
   \left(\frac{2r}{r}\right)^3 = 2^3 = 8
   $$

4. Therefore, the ratio of their volumes is  
   $$
   8:1
   $$
The ratio of their volumes is $$8:1$$.

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.

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