Question

A. A 5in radius ball is in a

box such that all six sides of
the box are touching the ball.
What percent of the space in
the box is being taken up by
the ball?

Answer 1

52.33%

Explanation:

Since, all six sides of the box are touching the ball.

So, all the three dimensions of the box are equal.

Hence, it is a cubical box.

Side length of the box (l)

= diameter of the ball

= 2*radius of the ball

= 2*5

= 10 In.

`V_(ball) = (4)/(3) \pi r^3`

`V_(ball) = (4)/(3) * 3.14(5)^3`

`V_(ball) = (4)/(3) * 3.14* 125`

`V_(ball) = (1,570)/(3)\: In^3`

`V_(box) =l^3`

`V_(box) =(10)^3`

`V_(box) =1000\: In^3`

Percentage of the space in the box occupied by the ball

`= (V_(ball))/(V_(box) ) * 100`

`= ((1,570)/(3))/(1000) * 100`

`= (1570)/(3000) * 100`

`= (157)/(3)`

`= 52.33\%`