The surface area of a sphere is \(\frac{792}{7} cm^2\). Find, correct to the nearest whole number, its volume. [Take \(\pi = \frac{22}{7}\)]
Answer Details
The formula for the surface area of a sphere is \(4\pi r^2\), where \(r\) is the radius of the sphere.
Given that the surface area of the sphere is \(\frac{792}{7} cm^2\) and \(\pi = \frac{22}{7}\), we can set up an equation:
$$
4\left(\frac{22}{7}\right)r^2 = \frac{792}{7}
$$
Simplifying this equation by canceling out the \(7\)s, we get:
$$
4\left(\frac{22}{1}\right)r^2 = 792
$$
Multiplying both sides by \(\frac{1}{4}\) to isolate \(r^2\), we get:
$$
\left(\frac{22}{1}\right)r^2 = 198
$$
Dividing both sides by \(\frac{22}{1}\), we get:
$$
r^2 = 9
$$
Taking the square root of both sides, we get:
$$
r = 3
$$
Therefore, the radius of the sphere is 3 cm.
The formula for the volume of a sphere is \(\frac{4}{3}\pi r^3\). Substituting the value of \(r\) into this formula, we get:
$$
\frac{4}{3}\left(\frac{22}{7}\right)(3)^3 \approx 113
$$
Therefore, the volume of the sphere is approximately 113\(cm^3\).
So the correct answer is 113\(cm^3\).