Chapter 12.6, Problem 11PPS

To determine

Calculate the surface area of mailing box and mailing tube and state object having smaller surface area.

Answer to Problem 11PPS

Mailing box has smaller surface area than mailing tube.

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 mailing tube

h is the height of mailing tube

Putting values in equation, we get

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times 5^2)+(2\times \pi \times 5\times 36)\\ =157.07+1130.97\\ =1288.04i{n}^2\end{array}$

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

  $\begin{array}{l}Surfacearea=2(width\times length)+2(length\times height)\\ =2(10\times 24)+2(24\times 12)\\ =480+576\\ =1056i{n}^2\end{array}$

Though mailing box and mailing tube have same volume, but their surface areas are different.

Surface area of mailing tube > surface area of mailing box.

Conclusion:

Therefore, we are able to calculate surface area of mailing box and mailing tube using simple formulae.