Atoy 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?

The volume of the empty space is

Step-by-step 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

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

substitute

step 2

Find the volume of the soccer ball

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

we have

substitute

step 3

Find the volume of the empty space

25

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: