Answer
The surface area and volume of the cement block are \[560\text{ in}{{\text{.}}^{\text{2}}}\] and\[576\text{ in}{{\text{.}}^{\text{3}}}\], respectively.
Work Step by Step
To compute the volume of the entire cement block, first compute the volume of one individual cement blocks and then multiply the volume of that one cement block with three.
The length, width, and height of the one individual cement block are 6 in., \[4\text{ in}\text{.}\], and \[8\text{ in}\text{.}\], respectively.
Compute the volume of one cement block using the equation as shown below:
\[\begin{align}
& \text{Volume of one cement block}=lwh \\
& =\left( \text{6 in}\text{.}\times \text{4 in}\text{.}\times \text{8 in}\text{.} \right) \\
& =\text{192 i}{{\text{n}}^{\text{3}}}
\end{align}\]
Now, compute the volume of the entire block using the equation as shown below:
\[\begin{align}
& \text{Volume of the entire cement block}=3\times \text{Volume of 1 cement block} \\
& =\left( 3\times 192\text{ i}{{\text{n}}^{\text{3}}} \right) \\
& =576\text{ i}{{\text{n}}^{\text{3}}}
\end{align}\]
Now, considering the surface area of the entire cement block, the dimensions that are length, breath, and height are \[8\text{ in}\text{.}\], \[16\text{ in}\text{.}\], and \[8\text{ in}\text{.}\], respectively.
To compute the surface area of the cement block, first compute the area of the four walls, second compute the area of the base, and third compute the total area of the horizontal strip along the length on the top. Last, compute the area of the strip along the width of the top. In this way, the total surface area of the cement block will be equal to the sum of all the aforesaid areas.
Now, compute the area of four walls using the equation as shown below:
\[\begin{align}
& {{A}_{1}}=2\left( l+b \right)h \\
& =2\left( 16\text{ in}+8\text{ in} \right)8\text{ in} \\
& =384\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
Now, compute the area of the base using the equation as shown below:
\[\begin{align}
& {{A}_{1}}=l\times b \\
& =16\text{ in}\text{.}\times 8\text{ in}\text{.} \\
& =128\text{ i}{{\text{n}}^{\text{2}}}
\end{align}\]
Now, compute the total area of the horizontal strip along the length on the top using the equation as shown below:
\[\begin{align}
& {{A}_{t}}=2\times b\times h \\
& =2\text{ in}\text{.}\times 16\text{ in}\text{.}\times 1 \\
& =32\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
Now, compute the total area of the strip along the width of the top using the equation as shown below:
\[\begin{align}
& {{A}_{w}}=4\text{ in}\text{.}\times 4\text{ in}\text{.}\times 1 \\
& =16\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
Finally, compute the total surface area of the cement block using the equation as shown below:
\[\begin{align}
& A={{A}_{1}}+{{A}_{2}}+{{A}_{t}}+{{A}_{w}} \\
& =384\text{ i}{{\text{n}}^{\text{2}}}+128\text{ i}{{\text{n}}^{\text{2}}}+\text{32 i}{{\text{n}}^{\text{2}}}+16\text{ i}{{\text{n}}^{\text{2}}} \\
& =560\text{ i}{{\text{n}}^{\text{2}}}
\end{align}\]
Hence, the volume and surface area of the cement block are \[560\text{ in}{{\text{.}}^{\text{2}}}\] and \[576\text{ in}{{\text{.}}^{\text{3}}}\] respectively.
