Express the volume of a rectangular solid (box) whose height, width and length are x,2x and 3x, respectively, as a function of its width.
To express the volume of a rectangular solid (box) as a function of its width, you need to use the given dimensions of the box and follow these steps:
1. Start by understanding the dimensions of the rectangular solid. The height is x, the width is 2x, and the length is 3x.
2. The volume of a rectangular solid is calculated by multiplying its three dimensions together: V = l × w × h. In this case, the volume (V) is equal to x × 2x × 3x.
3. Simplify the expression by multiplying the dimensions together: V = 6x^3.
4. Now, you want to express the volume (V) as a function of the width (w). Since the width is represented by 2x, substitute 2x for w in the volume equation: V = 6(2x)^3.
5. Simplify the expression by evaluating the exponent: V = 6(8x^3).
6. Finally, simplify the expression further: V = 48x^3.
Therefore, the volume of the rectangular solid, expressed as a function of its width, is V = 48x^3.