We appreciate your visit to Find the volume of a rectangular prism if the length is tex 4x tex the width is tex 2x tex and the height is tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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. In the problem, the dimensions are given as follows:
- Length [tex]\( l = 4x \)[/tex]
- Width [tex]\( w = 2x \)[/tex]
- Height [tex]\( h = x^3 + 3x + 6 \)[/tex]
To calculate the volume, multiply these expressions:
1. First, calculate the product of the length and the width:
[tex]\[ l \cdot w = (4x) \cdot (2x) = 8x^2 \][/tex]
2. Next, multiply this result by the height:
[tex]\[ 8x^2 \cdot (x^3 + 3x + 6) \][/tex]
3. Distribute [tex]\( 8x^2 \)[/tex] across the terms in the height expression:
[tex]\[
\begin{align*}
8x^2 \cdot x^3 & = 8x^{2+3} = 8x^5 \\
8x^2 \cdot 3x & = 24x^{2+1} = 24x^3 \\
8x^2 \cdot 6 & = 48x^{2} \\
\end{align*}
\][/tex]
4. Combining these results gives the volume:
[tex]\[ 8x^5 + 24x^3 + 48x^2 \][/tex]
Therefore, the volume of the rectangular prism is [tex]\( 8x^5 + 24x^3 + 48x^2 \)[/tex].
[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. In the problem, the dimensions are given as follows:
- Length [tex]\( l = 4x \)[/tex]
- Width [tex]\( w = 2x \)[/tex]
- Height [tex]\( h = x^3 + 3x + 6 \)[/tex]
To calculate the volume, multiply these expressions:
1. First, calculate the product of the length and the width:
[tex]\[ l \cdot w = (4x) \cdot (2x) = 8x^2 \][/tex]
2. Next, multiply this result by the height:
[tex]\[ 8x^2 \cdot (x^3 + 3x + 6) \][/tex]
3. Distribute [tex]\( 8x^2 \)[/tex] across the terms in the height expression:
[tex]\[
\begin{align*}
8x^2 \cdot x^3 & = 8x^{2+3} = 8x^5 \\
8x^2 \cdot 3x & = 24x^{2+1} = 24x^3 \\
8x^2 \cdot 6 & = 48x^{2} \\
\end{align*}
\][/tex]
4. Combining these results gives the volume:
[tex]\[ 8x^5 + 24x^3 + 48x^2 \][/tex]
Therefore, the volume of the rectangular prism is [tex]\( 8x^5 + 24x^3 + 48x^2 \)[/tex].
Thanks for taking the time to read Find the volume of a rectangular prism if the length is tex 4x tex the width is tex 2x tex and the height is tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
