Question

Please answer parts c and d. Show working as well. Thanks!

Answer 1

the volume of each spherical ball is
523.6 cm^3

and the volume of the box is 60,000 cm^3

a) the answer is 60

in each 10 cm of the rectangular prism you can place one sphere. so the answer of a is (4*3*5)

b) the answer is 30

c) the answer is 31,416

`60 * 523.6 = 31416`

d) 31,416 is 52.36% of 60,000

so the percentage of empty space is

100 - 52= 48%

good luck

Answer 2

Part C and D are dependent on Part A and B. So I have worked out from the beginning.

Part a:
Number of balls at the bottom layer = 3 x 4 = 12

Answer: 12 balls
Part b:
Number of balls in the box = 12 x 5 = 60

Answer: 60 balls

Part c:
Volume of 1 ball = 4/3π(5)³ = 523.60cm³
Volume of 60 balls = 523.60 x 60 = 31416 cm³

Answer: 31416 cm³

Part d:
Volume of the rectangular prism = 50 x 30 x 40 = 60 000 cm³
Volume of the space is empty = 60 000 - 31416 = 28584 cm³

Percentage of the box that is empty = 28584/60000 x 100 = 48%

Answer: 48%