The surface area of a sphere is \(\frac{792}{7} cm^2\). Find, correct to the nearest whole number, its volume. [Take \(\pi = \frac{22}{7}\)]
-
113\(cm^3\)
- 131\(cm^3\)
- 311\(cm^3\)
- 414\(cm^3\)
The correct answer is: A
Explanation
Surface area of a sphere = \(4 \pi r^2\)
\(4 \pi r^2\) = \(\frac{792}{7}cm^2\)
4 x \(\frac{22}{7}\) x \(r^2\) = \(\frac{792}{7}\)
\(r^2\) = \(\frac{792}{7}\) x \(\frac{7}{4 \times 22}\)
= 9
r = \(\sqrt{9}\)
= 3cm
Hence, volume of sphere
= \(\frac{4}{3} \pi r^3\)
= \(\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3 \)
= \(\frac{4 \times 22 \times 9}{7}\)
\(\approx\) = 113.143
= 113\(cm^3\) (to the nearest whole number)