Answer: The correct option is (C) 382 in³.
Step-by-step explanation: Given that a regulation basketball has a diameter of about 9 inches.
We are to select the best approximation of the volume of the ball.
We know that basketball is of the shape of a SPHERE.
The VOLUME of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
The diameter of the basketball is about 9 inches, so its approximate radius will be
[tex]r=\dfrac{9}{2}=4.5~\textup{inches}.[/tex]
Therefore, the approximate volume of the basketball is
[tex]V\\\\\\=\dfrac{4}{3}\pi r^3\\\\\\=\dfrac{4}{3}\times 3.14\times (4.5)^3\\\\\\=\dfrac{4\times3.14\times 91.125}{3}\\\\\\=381.51~\textup{in}^3~\textup{[approx.]}\sim 382~\textup{in}^3.[/tex]
Thus, the best approximation of the volume of the ball is 382 in³.
Thus, (C) is the correct option.
