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 the relationship between the volume of a ball and the dimensions of a box.
The volume of a ball is given by the formula:
V = (4/3) * π * r^3,
where V is the volume and r is the radius of the ball.
In this case, the volume V of the ball is 288π cm^3. So, we have:
288π = (4/3) * π * r^3.
We can cancel out π from both sides of the equation, which gives us:
288 = (4/3) * r^3.
Now, let's solve for r:
r^3 = (3/4) * 288,
r^3 = 216.
To find the radius, we can take the cube root of both sides of the equation:
r = ∛(216),
r ≈ 6 cm.
The radius of the ball is approximately 6 cm.
Now, let's determine the dimensions of the rectangular box. Since the ball is a sphere, the diameter of the sphere is equal to twice the radius. Therefore, the diameter of the sphere is 2 * 6 cm = 12 cm.
For the rectangular box to be just large enough to hold the ball, the dimensions of the box should be equal to or slightly larger than the diameter of the ball.
Therefore, the dimensions of the rectangular box that can hold the ball are:
Length = 12 cm,
Width = 12 cm, and
Height = 12 cm.
So, the dimensions of the rectangular box are 12 cm x 12 cm x 12 cm.