Chapter 12.6, Problem 15PPS

To determine

Calculate the surface area of given figure.

  

Answer to Problem 15PPS

Surface area of figure is $5474.23c{m}^2$

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate surface area. Given figure consist of three different parts via one rectangular prism and two cylindrical bars.

We know that, surface area of rectangular prism is calculated as,

  $\begin{array}{l}Surfacearea=2(width\times length)+2(length\times height)\\ =2(20\times 60)+2(60\times 15)\\ =2400+1800\\ =4200c{m}^2\end{array}$

We know that, surface area of cylinder 1 is calculated as,

  $Surfacearea=2\pi r^2+2\pi rh$

Where, r is the radius of cylinder

h is the height of cylinder

Putting values in equation, we get

  $\begin{array}{l}{\left(Surfacearea\right)}_1=2\pi r^2+2\pi rh\\ =(2\times 3.14\times {3.5}^2)+(2\times 3.14\times 3.5\times 15)\\ =76.93+329.7\\ {\left(Surfacearea\right)}_1=406.63c{m}^2\end{array}$

Now, surface area of cylinder 2 is calculated as,

  $\begin{array}{l}{\left(Surfacearea\right)}_2=2\pi r^2+2\pi rh\\ =(2\times 3.14\times {10}^2)+(2\times 3.14\times 10\times 7)\\ =628+439.6\\ {\left(Surfacearea\right)}_2=1067.6c{m}^2\end{array}$

Total surface area of figure given is,

  $\begin{array}{l}\left(TotalSurfacearea\right)=\left(Surfaceareaofrec\tan gularprism\right)+{\left(Surfacearea\right)}_1+{\left(Surfacearea\right)}_1\\ =(4200)+(406.63)+(1067.6)\\ =5474.23c{m}^2\end{array}$

Conclusion:

Therefore, we are able to calculate surface area of given figure using simple formula.