Chapter 12, Problem 26SGR

To determine

To calculate:To find the lateral and surface area of prism and round to the nearest tenth

Answer to Problem 26SGR

Lateral surface area of prism is $720in{.}^2$ and total surface area of prism is $810in{.}^2$

Explanation of Solution

Given information:Prism is

  

Formula Used:

Lateral and surface area of cuboid is given by the below formula:

  $Lateralsurfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)$

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Calculation:

Prims is given as follows

  

Here, dimensions of prism

as follows:

  $\begin{array}{l}Length=15in.\\ Width=3in.\\ Height=20in.\end{array}$

Lateral surface is calculated as follows:

  $Lateralsurfacearea=2\left(Length\times Height\right)+2\left(Width\times Height\right)$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfacearea=2\left(15\times 20\right)+2\left(3\times 20\right)\\ Lateralsurfacearea=2\left(300\right)+2\left(60\right)\\ Lateralsurfacearea=600+120\\ Lateralsurfacearea=720in{.}^2\end{array}$

Surface area is calculated as follows:

  $Surfaceare{a}_{Cuboid}=2\left(Length\times Height\right)+2\left(Width\times Height\right)+2\left(Width\times Length\right)$

Substituting the values, volume is

  $\begin{array}{l}Surfacearea=2\left(15\times 20\right)+2\left(3\times 20\right)+2\left(15\times 3\right)\\ Surfacearea=2\left(300\right)+2\left(60\right)+2\left(45\right)\\ Surfacearea=600+120+90\\ Surfacearea=810in{.}^2\end{array}$

Conclusion:

Hence, Lateral surface area of prism is $720in{.}^2$ and total surface area of prism is $810in{.}^2$