What is the length, in units, of the radius of a sphere whose volume and surface area, in cubic units and square units, respectively, are numerically equal?
I know that the volume of a sphere is given by V = (4/3)πr^3, where r is the radius, and the surface area of a sphere is given by A = 4πr^2, where r is the same radius. The problem asks me to find r when V and A are numerically equal, so I can set them equal to each other and solve for r. That is, (4/3)πr^3 = 4πr^2. To simplify this equation, I can divide both sides by 4πr^2, as long as r is not zero, which would make the sphere degenerate. This gives me (1/3)r = 1, or r = 3. Therefore, the radius of the sphere is 3 units. 