Question

Choose the correct answer of the following question:

If the surface area of a sphere is 616 cm², its diameter (in cm) is

(a) 7 (b) 14 (c) 28 (d) 56 [CBSE 2012]

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere}\mathrm{be}r. \\ \mathrm{As}, \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sphere}=616{\mathrm{cm}}^2 \\ \Rightarrow 4\mathrm{\pi }{r}^2=616 \\ \Rightarrow 4\times \frac{22}{7}\times r^2=616 \\ \Rightarrow r^2=\frac{616\times 7}{4\times 22} \\ \Rightarrow r^2=49 \\ \Rightarrow r=\sqrt{49} \\ \Rightarrow r=7\mathrm{cm} \\ \therefore \mathrm{Diameter}\mathrm{of}\mathrm{the}\mathrm{sphere}=2r=2\times 7=14\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (b).