Dimensions of Box 2: [tex]x[/tex] by [tex]4x - 1[/tex] by [tex]x^3[/tex]

The volume of Box 2 is given by:

A. [tex]4x^5 - x^4[/tex]

B. [tex]4x^6 - x^3[/tex]

C. [tex]4x^5 + x^4[/tex]

D. [tex]x^3 + 5x - 1[/tex]

Answer :

Sure, let's solve the problem step by step!

We are given the dimensions of Box 2 as:
- Length: [tex]\( x \)[/tex]
- Width: [tex]\( 4x - 1 \)[/tex]
- Height: [tex]\( x^3 \)[/tex]

To find the volume of the box, we need to multiply these dimensions together. The formula for the volume [tex]\(V\)[/tex] is:

[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]

Substituting the given dimensions into the formula, we get:

[tex]\[ V = x \times (4x - 1) \times x^3 \][/tex]

Now, let's simplify this step by step:

1. Multiply the length and width together:
[tex]\[ x \times (4x - 1) = 4x^2 - x \][/tex]

2. Now, multiply the result by the height:
[tex]\[ (4x^2 - x) \times x^3 \][/tex]

This can be further expanded as:
[tex]\[ 4x^2 \times x^3 - x \times x^3 \][/tex]
[tex]\[ 4x^5 - x^4 \][/tex]

So, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]

Let's match this with the given choices:
1. [tex]\( 4x^5 - x^4 \)[/tex]
2. [tex]\( 4x^6 - x^3 \)[/tex]
3. [tex]\( 4x^5 + x^4 \)[/tex]
4. [tex]\( x^3 + 5x - 1 \)[/tex]

The correct choice corresponds to [tex]\( 4x^5 - x^4 \)[/tex].

Therefore, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]

And the correct choice is 1.