Explanation:
Let r be the radius of both the sphere and the cylinder, and let V be their common volume. The volume of a sphere with radius r is (4/3)πr^3, and the volume of a right cylinder with radius r and height 8 is πr^2(8) = 8πr^3. Since the sphere and the cylinder have the same volume, we can set these expressions equal to each other:
(4/3)πr^3 = 8πr^3
Dividing both sides by πr^3 and simplifying, we get:
4/3 = 8
This is a contradiction, since 4/3 is not equal to 8. Therefore, there is no common radius that would make the sphere and the cylinder have the same volume.