Answer: D
Let the radius of the second sphere be \(r\) units. \(\therefore\) The radius of the first sphere is \(2r\) units. \(\therefore\) Surface area of the first sphere: \(4\pi(2r)^2 = \frac{4}{3}\pi r^3\) Or, \(16\pi r^2 = \frac{4}{3}\pi r^3\) Dividing both sides by \(\pi\): \(16r^2 = \frac{4}{3}r^3\) Simplifying: \(4 = \frac{r}{3}\) Solving for \(r\): \(r = 12\) \(\therefore\) The radius of the first sphere = \(2r = 2 \times 12 = 24\) units.
Let the radius of the second sphere be \(r\) units. \(\therefore\) The radius of the first sphere is \(2r\) units. \(\therefore\) Surface area of the first sphere: \(4\pi(2r)^2 = \frac{4}{3}\pi r^3\) Or, \(16\pi r^2 = \frac{4}{3}\pi r^3\) Dividing both sides by \(\pi\): \(16r^2 = \frac{4}{3}r^3\) Simplifying: \(4 = \frac{r}{3}\) Solving for \(r\): \(r = 12\) \(\therefore\) The radius of the first sphere = \(2r = 2 \times 12 = 24\) units.