Q.The diameter of one sphere is twice the diameter of another sphere. The curved surface area of the first sphere is equal to the volume of the second sphere. What is the radius of the first sphere? (a) 21 (b) 22 (c) 23 (d) 24
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.
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