Solution:
To calculate the surface area, we will use the formula below
The lateral surface area of a cuboid is the value of the surface area of a cuboid excluding its top and bottom surfaces. The formula for the lateral surface area of a cuboid is expressed as,
[tex]\begin{gathered} L.A=2h(l+w) \\ h=3in \\ l=8in \\ w=6in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} L.A=2h(l+w) \\ L.A=2(3)(8+6) \\ L.A=6(14)in^2 \\ L.A=84in^2 \end{gathered}[/tex]Hence,
The lateral area is
[tex]\Rightarrow84in^2[/tex]Part B:
Since the shape of the cuboid is a rectangle, to figure out the area of the single base, we will
use the formula below
[tex]\begin{gathered} Area\text{ }of\text{ }single\text{ }base=l\times b \\ l=8in,b=6in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} Areaofsinglebase=l\times b \\ Areaofsinglebase=8in\times6in \\ Areaofsinglebase=48in^2 \end{gathered}[/tex]Hence,
The area of the single base is
[tex]\Rightarrow48in^2[/tex]Part C:
To figure out the total surface area of the cuboid, we will use the formula below
[tex]\begin{gathered} S.A=2(lw+lh+wh) \\ S.A=2(8\times6)+(8\times3)+(6\times3) \\ S.A=2(48+24+18) \\ S.A=2(90) \\ S.A=180in^2 \\ \\ Alternatively, \\ S.A=lateral\text{ }area+2(area\text{ }of\text{ }base) \\ S.A=84in^2+2(48in^2) \\ S.A=84in^2+96in^2 \\ S.A=180in^2 \end{gathered}[/tex]Hence,
The total surface area is
[tex]\Rightarrow180in^2[/tex]