. A toy company is selling novelty soccer balls of all sizes. If one soccer ball, with a radius of 5 cm, is placed in a box with all equal dimensions, as shown below, and the ball is touching the sides of the box, approximately how much empty space is inside the box?

Answer:The volume of the empty space is [tex]476.67\ cm^{3}[/tex]Step-by-step explanation:we know thatThe volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ballstep 1 Find the volume of the boxThe length side of the cube is equal to the diameter of the soccer ballLetb -----> the length side of the boxwe have[tex]b=2r=2(5)=10\ cm[/tex]The volume of the box is equal to the volume of a cube[tex]V=b^{3}[/tex]substitute[tex]V=10^{3}[/tex][tex]V=1,000\ cm^{3}[/tex]step 2Find the volume of the soccer ballThe volume of the sphere (soccer ball) is equal to[tex]V=\frac{4}{3}\pi r^{3}[/tex]we have[tex]r=5\ cm[/tex][tex]\pi =3.14[/tex]substitute[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex][tex]V=523.33\ cm^{3}[/tex]step 3Find the volume of the empty space[tex]V=1,000-523.33=476.67\ cm^{3}[/tex]