This is a geometry question involving volume and a cube.

Question

teri has an aquarium that is a cube with edge lengths of 24 inches. the aquarium is 2/3 full of water she has a supply of ball bearings each having a diameter of 3/4 what is the maximum number of ball bearings that teri can drop into the aquarium without the water overflowing?

 

Please help I do not understand this problem !!

Answer 1

V=(4/3)∏r^3 where r=3/8

V=0.22089 cubic inches for each ball bearing

24*24*24=13,824, and 13,824/3=4608 cubic inches not filled with water

the volume available to fill and overflow is 4608 cubic inches

24/(3/4)=32 ball bearings across and down for a total of 32*32=1024 ball bearings per one layer

the volume of each ball bearing is 0.22089 cubic inches

0.22089*1024=226.19 cubic inches for the volume of one layer

one layer takes up 226.19 cubic inches so 226.19 cubic inches of water is displaced

4608/226.19=20.372253 layers of ball bearings are needed

20.372253*1024=20,861.187 ball bearings are needed to overflow the water

therefore you can put 20,861 ball bearings in the tank without overflowing the water 

Answer 2

V = e³

V = 24³

V = 13824

 

Volume available is 13824 / 3, or 4608

 

V = 4πr³/3

V = 4π(0.375)³ / 3

V = 4π(0.052734) / 3

V = 4π(0.017578)

V = 0.070π

V = 0.22

 

Here we encounter a conflict between algebra and reality.

In algebra I would divide the volume available by the volume of each bearing.

Yet bearings rest with empty space between them.

As such an accurate answer is not possible.