If the volume of a sphere is 4851$cm^{3}$ then its surface area (in $cm^{2}$) is: (Take $\pi = \frac{22}{7}$)
Answer & explanation
Correct answer: option 2
We know that,
Surface area of sphere = 4πr2
Volume of sphere = \(\frac{4}{3}\)πr3
The volume of the sphere = 4851 cm3
Volume of sphere = 4851 = \(\frac{4}{3}\)× \(\frac{22}{7}\)× r3
= r3 = 441 × \(\frac{21}{8}\)
= r = \(\frac{21}{2}\)
Surface area of sphere = 4 × \(\frac{22}{7}\)× (\(\frac{21}{2}\))2
= 4 × \(\frac{22}{7}\)× \(\frac{441}{8}\)
= 22 × 63 = 1386