The Bown-C Balls company manufactures balls with a circumference that measures 13 inches. They want to package the balls in the smallest possible cube-shaped box. To the hundreths place, what is the length of the side of the smallest box that can hold a ball
2.07 in
4.14 in
6.21 in
6.50 in
the ball diameter is ... circumference / π
So what is the diameter?
pi D = 13
so
D = 13 / 3.14159 = about 4.138 will work :)
thanks for the help! greatly appreciated
You are welcome.
To find the side length of the smallest cube-shaped box that can hold a ball, we first need to understand the relationship between the circumference of a ball and the side length of a cube.
The formula to find the circumference of a sphere (ball) is C = 2πr, where C is the circumference and r is the radius of the sphere.
Since we are given the circumference of the ball (13 inches), we can rearrange the formula to solve for the radius of the ball:
C = 2πr
13 = 2πr
r = 13 / (2π)
Next, we need to determine the diameter of the ball, which is twice the radius:
d = 2r
d = 2 * (13 / (2π))
d = 13 / π
Finally, we can determine the side length of the cube by using the diameter of the ball. Since all sides of a cube are equal, we have:
side length of cube = diameter of ball = 13 / π
Now, let's calculate it:
side length of cube = 13 / π ≈ 4.14 inches
Therefore, the correct answer is 4.14 inches.