Chapter 12.6, Problem 17PPS

To determine

States whether rectangular or cylindrical container should Student Council buy to reduce costing.

Answer to Problem 17PPS

Surface area of rectangular container is lesser than that of cylindrical container. Therefore, student council must buy rectangular container so as to reduce costing.

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate surface area of cylinder and rectangular prism.

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

  $Surfacearea=2\pi r^2+2\pi rh$

Where, $r$ is the radius of cylinder

h is the height of cylinder

We will calculate surface area of cylindrical popcorn container,

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times 3^2)+(2\times \pi \times 3\times 9.7)\\ =56.54+182.84\\ =239.38i{n}^2\end{array}$

Now, surface area of rectangular popcorn container is calculated as,

  $\begin{array}{l}Surfacearea=2(width\times length)+2(length\times height)\\ =2(5.5\times 5)+2(5\times 10)\\ =55+100\\ =155i{n}^2\end{array}$

Amount of cardboard required to make container is equal to surface area of container. Surface area of rectangular container is lesser than that of cylindrical container. As costing depends on the amount of cardboard required, rectangular container needs minimum cardboard.

Conclusion:

Therefore, we are able to calculate surface area of containers having different shapes using simple formulae.