To find the volume of a rectangular prism, we need to multiply lenght by height by width:
[tex]V=2\operatorname{cm}\cdot3\operatorname{cm}\cdot4\operatorname{cm}=24\operatorname{cm}^3[/tex]To find the surface area, we need to calculate the area of each of the rectangles.
We have:
2 rectangles 3cm by 4cm
2 rectangles 4cm by 2 cm
2 rectangles 2cm by 3cm
Then we calculate the area of each one:
[tex]\begin{gathered} 3cm\cdot4\operatorname{cm}=12\operatorname{cm}^2 \\ 4\operatorname{cm}\cdot2\operatorname{cm}=8\operatorname{cm}^2 \\ 2\operatorname{cm}\cdot3\operatorname{cm}=6\operatorname{cm}^2 \end{gathered}[/tex]Since there are 2 of each, we multiply each by 2:
[tex]\begin{gathered} 2\cdot12\operatorname{cm}=24\operatorname{cm}^2 \\ 2\cdot8\operatorname{cm}=16\operatorname{cm}^2 \\ 2\cdot6\operatorname{cm}=12\operatorname{cm}^2 \end{gathered}[/tex]Finally we add the areas:
[tex]24\operatorname{cm}+16\operatorname{cm}+12\operatorname{cm}=52\operatorname{cm}^2[/tex]Then the volume is 24cm^3 and the surface area is 52cm^2
