If the volume of a sphere is 179$\frac{2}{3}$ m3, what is its surface area ?
Answer & explanation
Correct answer: option 2
We know that,
Volume of a sphere = \(\frac{4}{3}\) πr3
Surface area of a sphere = 4πr2
\(\frac{4}{3}\) πr3 = 179$\frac{2}{3}$
\(\frac{4}{3}\) πr3 = \(\frac{539}{3}\)
= 4πr3 = 539
= 4 × \(\frac{22}{7}\) × r3 = 539
= 4 × \(\frac{2}{7}\) × r3 = 49
= r3 = 49×\(\frac{7}{8}\)
= r = 3.5
Surface area = 4 × \(\frac{22}{7}\) × 3.52 = 154 m2