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Answer :
To find the volume of a rectangular prism, we use the formula [tex]\( V = l \cdot w \cdot h \)[/tex], where [tex]\( l \)[/tex] is the length, [tex]\( w \)[/tex] is the width, and [tex]\( h \)[/tex] is the height.
Given:
- Length [tex]\( l = 4x \)[/tex]
- Width [tex]\( w = 2x \)[/tex]
- Height [tex]\( h = x^3 + 3x + 6 \)[/tex]
Let's compute the volume step-by-step:
1. Multiply the Length and Width:
[tex]\[
l \cdot w = 4x \cdot 2x = 8x^2
\][/tex]
2. Multiply by the Height to find the Volume:
[tex]\[
V = 8x^2 \cdot (x^3 + 3x + 6)
\][/tex]
3. Distribute [tex]\( 8x^2 \)[/tex] Across Each Term in the Parentheses:
- First Term:
[tex]\[
8x^2 \cdot x^3 = 8x^{2+3} = 8x^5
\][/tex]
- Second Term:
[tex]\[
8x^2 \cdot 3x = 24x^{2+1} = 24x^3
\][/tex]
- Third Term:
[tex]\[
8x^2 \cdot 6 = 48x^2
\][/tex]
4. Combine These Results:
[tex]\[
V = 8x^5 + 24x^3 + 48x^2
\][/tex]
So, the volume of the rectangular prism is [tex]\( 8x^5 + 24x^3 + 48x^2 \)[/tex].
Therefore, the correct answer is:
[tex]\[ 8x^5 + 24x^3 + 48x^2 \][/tex]
Given:
- Length [tex]\( l = 4x \)[/tex]
- Width [tex]\( w = 2x \)[/tex]
- Height [tex]\( h = x^3 + 3x + 6 \)[/tex]
Let's compute the volume step-by-step:
1. Multiply the Length and Width:
[tex]\[
l \cdot w = 4x \cdot 2x = 8x^2
\][/tex]
2. Multiply by the Height to find the Volume:
[tex]\[
V = 8x^2 \cdot (x^3 + 3x + 6)
\][/tex]
3. Distribute [tex]\( 8x^2 \)[/tex] Across Each Term in the Parentheses:
- First Term:
[tex]\[
8x^2 \cdot x^3 = 8x^{2+3} = 8x^5
\][/tex]
- Second Term:
[tex]\[
8x^2 \cdot 3x = 24x^{2+1} = 24x^3
\][/tex]
- Third Term:
[tex]\[
8x^2 \cdot 6 = 48x^2
\][/tex]
4. Combine These Results:
[tex]\[
V = 8x^5 + 24x^3 + 48x^2
\][/tex]
So, the volume of the rectangular prism is [tex]\( 8x^5 + 24x^3 + 48x^2 \)[/tex].
Therefore, the correct answer is:
[tex]\[ 8x^5 + 24x^3 + 48x^2 \][/tex]
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