Question

A 4ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 42ft3. Use the ALEKS graphing calculator to find the side length of the original cube. Round your answer to two decimal places.

Answer 1

Answer:

The side length of the original cube is 5.43 ft

Step-by-step explanation:

Let x be the edge ( in feet ) of the cube,

∵ Volume of a cube = side³,

Thus, the volume of the given cube,

$V=x^3$

Now, 4ft thick slice is cut off the top of a cube,

The volume of the slice = x × x × 4 = 4x² ft²,

Thus, the volume of the resulting figure = volume of cube - volume of cut figure

= ( x³ - 4x² ) ft²

According to the question,

$x^3-4x^2=42$

$\implies x^3-4x^2-42=0$

The solution of the above equation will be obtained by finding the zeros of the function $f(x)=x^3-4x^2-42$ ( by graphing ),

We found that,

The graph of the equation intersect x at (5.426,0)

Thus, the zero of the equation is 5.426

⇒ x = 5.426 ≈ 5.43

Hence, the side length of the original cube is 5.43 ft ( approx )