What is its surface area of the sphere if the volume of the sphere is \(179\frac{2}{3}\) m3?
Solution
Correct Answer: Option A
Volume of the sphere is given by (4/3)π r3
Surface area of sphere is 4π r2
Given, volume of the sphere is \(179\frac{2}{3} = \frac{{539}}{3}\) m3
\(\begin{array}{l} \Rightarrow \left( {\frac{4}{3}} \right)\pi \;{r^3} = \left( {\frac{{539}}{3}} \right)\\ \Rightarrow r = {\left( {\frac{{539}}{{4\pi }}} \right)^{\frac{1}{3}}}m \end{array}\)
Now, Surface area of sphere is \(= \;4 \times \;\frac{{22}}{7} \times \;{\left( {\frac{{539}}{{4\pi }}} \right)^{\frac{2}{3}}} = 154{m^2}\)
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