Final answer:
The ratio of the volumes of the two spheres is 8.
Step-by-step explanation:
To find the ratio of the volumes of the two spheres, we need to compare their radii. Let's assume the radius of the second sphere is 'r'. According to the question, the radius of the first sphere is twice as great as the radius of the second sphere, meaning its radius is 2r.
The volume of a sphere is given by V = (4/3)πr³. Therefore, the volume of the first sphere is V₁ = (4/3)π(2r)³ = (4/3)π(8r³) = (32/3)πr³.
Similarly, the volume of the second sphere is V₂ = (4/3)πr³.
Now, to find the ratio of their volumes, we divide the volume of the first sphere by the volume of the second sphere: V₁/V₂ = [(32/3)πr³] / [(4/3)πr³] = 32/4 = 8.