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 = \(2r\) units. So, Surface area of the first sphere = \(4\pi(2r)^2\) Volume of the second sphere = \(\frac{4}{3}\pi r^3\) Equating the two: \[ 4\pi(2r)^2 = \frac{4}{3}\pi r^3 \] \[ 16\pi r^2 = \frac{4}{3}\pi r^3 \] \[ 4 = \frac{r}{3} \] \[ r = 12 \] \(\therefore\) Radius of the first sphere = \(2r = 2 \times 12 = 24\) units.
Similar Questions