Question

A 3in thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 47in3. Use the ALEKS graphing calculator to find the side length of the original cube. Round your answer to two decimal places.

Answer 1

Answer:

4.93 inches

Step-by-step explanation:

Let x be the side length ( in inches ) of the original cube,

∵ 3 in thick slice is cut off the cube,

So, the volume of the slice = 3 × x × x = 3x²,

Now, the volume of a cube = ( side length )³,

That is, the length of the given cube = x³

Thus, the volume of the resultant figure = volume of cube - volume of slice

= x³ - 3x²

According to the question,

$x^3-3x^2 = 47$

$x^3 - 3x^2 - 47 =0$

After plotting the function $x^3-3x^2-47$ in the graph,

We found that,

Zeros of the function is,

x = 4.932

Hence, the solution of the above equation is x = 4.932 ≈ 4.93

That is, the side length of the original cube is 4.93 in.