Question

Please help me solve the problem

Answer 1

Let x = the length of each side of the middle cube.

Without using the cube root function on the calculator, we shall iteratively find the value of x as follows:

We know that the volume is 30, and it lies between 27  and 64. Therefore x lies between 3  and 4.

Create a table as shown below.
We shall guess the value of x between iterations and calculate the volume as V = x*x*x.
When the absolute value of the difference between 30 and V is less than 0.5, we shall assume that the value of x is sufficiently accurate.
To make the next guess for x, we decrease x when V>30 and increase x when V<30.

Iteration                x          V=x*x*x       |V-30|    Decision
------------   ------------- -------------------   ------------   -------------
       1                  3.5           42.875      12.875    Lower x
       2                3.25          34.328       4.328    Lower x
       3               3.125          30.518         0.518   Lower x
       4           3.0625          28.723         1.277    Raise x
       5           3.0938          29.613         0.387    Good enough

Answer: The approximate length of the side is 3.0938.