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 a rectangular box that can hold the ball, we can use the formula for the volume of a sphere:
V = (4/3)pi r^3
where V is the volume of the sphere and r is the radius of the sphere.
In this case, the volume of the ball is given as 288 pi cm^3. Therefore, we can set up the equation:
288 pi = (4/3)pi r^3
To solve for r, we can cancel out the common factor of pi on both sides of the equation:
288 = (4/3) r^3
Next, we can simplify the equation:
3 * 288 = 4 r^3
864 = 4 r^3
To isolate r^3, we divide both sides of the equation by 4:
864 / 4 = r^3
216 = r^3
Now, to find the radius r, we can take the cube root of both sides of the equation:
∛216 = r
Simplifying the cube root of 216 gives us:
r ≈ 6
So, the radius of the ball is approximately 6 cm.
Now, to find the dimensions of the rectangular box, we can use the diameter of the ball as the longest dimension of the box. The diameter is twice the radius, so the longest dimension of the box is 2 * 6 = 12 cm.
For the other two dimensions, we can use the radius as the width and height of the box, so each of those dimensions will be 6 cm.
Therefore, the dimensions of the rectangular box that is just large enough to hold the ball are:
Length: 12 cm
Width: 6 cm
Height: 6 cm