Answer: \(\text{Volume}=288\pi\ in^3\)
Step-by-step explanation:
Given: The surface area of a beach ball =\(144\pi\ in^2\)
The surface area of sphere is given by :-
\(\text{SA}=4\pi r^2\\\\\Rightarrow144\pi=4\pi\ r^2\\\\\Rightarrow\ r^2=36\\\\\Rightarrow\ r=6\ in\)
We know that the volume of a sphere is given by :-
\(\text{Volume}=\dfrac{4}{3}\pi\ r^3\), where r is the radius of the sphere.
\(\Rightarrow\text{Volume}=\dfrac{4}{3}\pi (6)^3\\\\\Rightarrow\ \text{Volume}=288\pi\ in^3\)
Hence, the volume of air the beach ball will hold when it is fully inflated is \(288\pi\ in^3\)
