Question

. 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 1

The volume of the empty space is
`476.67\ cm^(3)`

Explanation:

we know that

The volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ball

step 1

Find the volume of the box

The length side of the cube is equal to the diameter of the soccer ball

Let

b -----> the length side of the box

we have

`b=2r=2(5)=10\ cm`

The volume of the box is equal to the volume of a cube

`V=b^(3)`

substitute

`V=10^(3)`

`V=1,000\ cm^(3)`

step 2

Find the volume of the soccer ball

The volume of the sphere (soccer ball) is equal to

`V=(4)/(3)\pi r^(3)`

we have

`r=5\ cm`

`\pi =3.14`

substitute

`V=(4)/(3)(3.14)(5)^(3)`

`V=523.33\ cm^(3)`

step 3

Find the volume of the empty space

`V=1,000-523.33=476.67\ cm^(3)`