Answer: \(1024\pi\ m^2\)
Step-by-step explanation:
The volume of a sphere is given by :-
\(\text{Volume}=\dfrac{4}{3}\pi\ r^3\), where r is the radius of the sphere.
Given: The volume of a sphere =\(5,000\pi\ m^3\)
\(\Rightarrow5000\pi=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ r^3=\dfrac{3}{4}\times5000\\\\\Rightarrow\ r^3=3750\\\\\Rightarrow\ r=15.536162\approx16\ m\)
The surface area of sphere is given by :-
\(\text{SA}=4\pi r^2\\\\\Rightarrow\text{SA}=4\pi(16)^2\\\\\Rightarrow\ SA=1024\pi\ m^2\)
