Park H.

asked • 07/16/20# sixteen perfectly spherical snooker balls fit tightly into the box. Find the percent of the box's volume that is NOT occupied by the balls. Use 3.14 for π

A)38.97%

B)47.64%

C)58.53%

D)72.12%

## 2 Answers By Expert Tutors

Mark M. answered • 07/16/20

Mathematics Teacher - NCLB Highly Qualified

r represents the radius of a ball

V_{box} = 4(2r)(4(2r)(2r)

V_{box }= 128r^{3}

V_{balls} = 16((4/3)πr^{3}

V_{balls} = 67.02r^{3}

V_{space} = 128r^{3} - 67.03r^{3}

V_{space} = 60.97r^{3}

What percent of the box is that?

Find the volume of the box. If the box is a cube, then the diameter of one ball is 1/4 of one side. Find the volume of one ball and multiply by 16 to get the total volume of the balls.

Subtract the volume of the balls from the volume of the box, then divide that difference by the volume of the box. Don't forget to multiply by 100 to get your percentage.

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Mark M.

Are the balls 16 in one 4 x 4 arrangement or in a two tiered arrangement?07/16/20