Final answer:
To determine the dimensions of a rectangular box that can hold a ball with a volume of 288π cm cubed, we calculate the radius of the sphere and find that the box must be a cube with dimensions 12 cm × 12 cm × 12 cm.
Step-by-step explanation:
To find the dimensions of a rectangular box that can hold a sphere with a volume of 288π cm cubed, we must first determine the radius of the sphere. We use the formula for a sphere's volume, V = ⅓πr³, where V is the volume and r is the radius.
Setting the given volume equal to the formula's volume, we have 288π = ⅓πr³. Cancelling the π on both sides and multiplying by 3 gives us r³ = 864. To find r, take the cube root of both sides to get r = 6 cm.
Since the ball must fit inside the box, the box dimensions will be twice the radius in each direction. Thus, the dimensions of the box are length = 12 cm, width = 12 cm, and height = 12 cm, forming a cube.