Given that the volume of a boys' basketball is 434 cubic inches, and Dan would like to get a ball with half the volume for his son, to determine what is the diameter of the ball that Dan will buy for his son, the following calculation has to be done, knowing that the volume of a sphere is four thirds multiplied by pi multiplied by the radius cubed:
4/3 x 3.14 x X ^ 3 = 434
4.186 x X ^ 3 = 434
X ^ 3 = 434 / 4.186
X = 3√ 103.662
X = 4.7
In turn, since the radius of a sphere is equal to half its diameter, the diameter of the basketball is 9.4 inches (4.7 x 2).
