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.
If the volume of the ball is 288 pic cubic inches, what is the diameter of the ball?
To find the dimensions of a rectangular box that is just large enough to hold the ball, we can start by considering the shape of the ball.
The volume of a ball is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the ball.
In this case, we are given the volume of the ball as 288π cm^3. Therefore, we can set up the equation:
288π = (4/3)πr^3
First, let's simplify the equation by canceling out the π on both sides:
288 = (4/3)r^3
Next, let's isolate r by multiplying both sides of the equation by 3/4:
r^3 = (288 * 3/4)
r^3 = 216
Now, find the cube root of both sides to solve for r:
r = ∛(216)
r = 6 cm
Now that we have the radius of the ball, we can determine the dimensions of the rectangular box that can hold the ball. The dimensions of the box will be twice the radius in each direction (length, width, and height) to provide enough space for the ball.
Length of the box = 2 * r = 2 * 6 = 12 cm
Width of the box = 2 * r = 2 * 6 = 12 cm
Height of the box = 2 * r = 2 * 6 = 12 cm
Therefore, the dimensions of the rectangular box that is just large enough to hold the ball are 12 cm x 12 cm x 12 cm.