In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
are the same size and packed wall-to-wall. If each of the tanks are filled to the top with water, which
tank would contain the most water. Prove your answer algebraically using x to represent the edge
length of the tanks.

Step-by-step explanation:

Let represent the edge of the tank with x and the radius of the first sphere with x/2;

The amount of the water = Volume of the tank - Volume of the sphere

=

on the second cube ; the radius of the sphere = ;

Also the number of sphere here is = 8

The amount of water =

For the third figure ; the radius of the sphere is =

Also the number of sphere here is = 64

The amount of water =

=

In the fourth tank ; 512 sphere illustrates that in a single row; that more than one 8 sphere is present i.e 8³ = 512

then the radius will be =

The amount of water =

=

This implies that alll the three cube shaped tanks are identical and hold equal amount of water.