A cue shaped box fits exactly around a soccerball with a diameter of 22.28 cm. What percent of the box is empty space?
Help understand how to get to the answer, and wat it would be
Cube shaped box*
To find the percent of space that is empty in the cube-shaped box, we first need to determine the volume of the cube and the volume of the soccer ball.
1. Calculate the volume of the cube:
Since it's a cube, all sides are equal in length. The length of each side can be found by considering the diameter of the soccer ball as the diagonal of one of the cube's faces.
The diagonal of a face of a cube can be found using the Pythagorean theorem. In this case, the length of each side (a) can be calculated as follows:
a = (sqrt(2) / 2) * diameter
a = (sqrt(2) / 2) * 22.28 cm
a ≈ 15.75 cm
Therefore, the volume of the cube is:
Volume = a^3 = 15.75 cm * 15.75 cm * 15.75 cm ≈ 3920.48 cm^3
2. Calculate the volume of the soccer ball:
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * (radius^3)
The radius of the soccer ball is half of its diameter, so:
radius = 22.28 cm / 2 = 11.14 cm
Hence, the volume of the soccer ball is:
Volume = (4/3) * π * (11.14 cm)^3 ≈ 6974.28 cm^3
3. Calculate the empty space:
Empty space = Volume of the cube - Volume of the soccer ball
Empty space = 3920.48 cm^3 - 6974.28 cm^3
Empty space ≈ -3053.80 cm^3
The negative value indicates that the soccer ball does not fit entirely within the cube, so there is no empty space.
Therefore, the percent of space that is empty in this scenario is 0%.