Questions: A 4 ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 21 ft^3. Use the ALEKS graphing calculator to find the side length of the original cube. Round your answer to two decimal places.

Solution Steps

We are given a cube with an unknown side length, and a 4 ft thick slice is cut off the top, resulting in a rectangular box with a volume of \(21 \, \text{ft}^3\). We need to find the original side length of the cube.

Let \(s\) be the side length of the original cube. The volume of the original cube is \(s^3\). After cutting a 4 ft thick slice from the top, the height of the remaining box is \(s - 4\) ft, and the base remains a square with side length \(s\).

The volume of the resulting rectangular box is given by: \[ s^2 \times (s - 4) = 21 \]

We need to solve the equation: \[ s^2(s - 4) = 21 \]

Expanding and rearranging gives: \[ s^3 - 4s^2 = 21 \]

Rearrange to form a standard polynomial equation: \[ s^3 - 4s^2 - 21 = 0 \]

Using a graphing calculator or numerical method, we find the root of the equation \(s^3 - 4s^2 - 21 = 0\).

The solution to the equation is approximately \(s = 5.34\) when rounded to two decimal places.

Final Answer