Question

In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank

Answer 1

Answer:

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

= $x^3 - \frac{4}{3} \pi (\frac{x}{2})^3$

on the second cube ; the radius of the sphere = $\frac{x}{4} \ units$ ;

Also the number of sphere here is = 8

The amount of water = $x^3 -8*\frac{4}{3} \pi (\frac{x}{4})^3$

For the third figure ; the radius of the sphere is = $\frac{x}{8} \ units$

Also the number of sphere here is = 64

The amount of water = $x^6 -64*\frac{4}{3} \pi (\frac{x}{8})^3$

= $x^3 - \frac{4}{3} \pi (\frac{x}{2})^3$

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 = $\frac{x}{16}$

The amount of water = $x^3 -512*\frac{4}{3} \pi (\frac{x}{16})^3$

= $x^3 -\frac{4}{3} \pi (\frac{x}{2})^3$

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