The volume of a ball is 288 pi cm^3. Find the dimensions of a rectangular box that is just large enough to hold the ball. Use 3.14 for pie
To find the dimensions of the rectangular box that can hold the ball, we need to consider that the ball is a sphere. The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
where V is the volume of the sphere and r is the radius.
In this case, we have the volume of the ball as 288π cm^3. Therefore, we can set up the equation:
288π = (4/3) * π * r^3
Dividing both sides of the equation by (4/3)π, we get:
r^3 = (288π * 3) / (4π)
Simplifying further:
r^3 = 216
Taking the cube root of both sides, we find the radius of the ball:
r = ∛216
r = 6 cm
Now that we have the radius, we can find the dimensions of the rectangular box. The maximum dimensions of the box will be twice the radius of the ball.
Therefore, the dimensions of the rectangular box are:
Length = 2r = 2 * 6 = 12 cm
Width = 2r = 2 * 6 = 12 cm
Height = 2r = 2 * 6 = 12 cm
So, the dimensions of the rectangular box that can hold the ball are 12 cm x 12 cm x 12 cm.