Chapter 12.6, Problem 4CYU

To determine

Calculate the surface area of orange juice can and soup can and state which can need more paper for labelling.

Answer to Problem 4CYU

Soup can will need more paper for labelling than orange juice can.

Explanation of Solution

Given:

For orange juice can:

Diameter = $2\frac{1}{2}inch$ ; Radius = 1.25 inch

Height= 5 inch

For soup can:

Radius = 2 inch

eight = 5.5 inch

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 orange juice can,

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times {1.25}^2)+(2\times \pi \times 1.25\times 5)\\ =9.817+39.26\\ =49.077i{n}^2\end{array}$

Lateral area of orange juice can is calculated as,

  $\begin{array}{l}LateralSurfacearea=2\pi rh\\ =(2\times \pi \times 1.25\times 5)\\ =39.26i{n}^2\end{array}$

We will calculate surface area of soup can,

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times 2^2)+(2\times \pi \times 2\times 5.5)\\ =25.132+69.11\\ =94.247i{n}^2\end{array}$

Lateral area of soup can is calculated as,

  $\begin{array}{l}LateralSurfacearea=2\pi rh\\ =(2\times \pi \times 2\times 5.5)\\ =69.11i{n}^2\end{array}$

Labelling is done on lateral surface area of can. Lateral surface area of soup can is more than orange juice can. Therefore, soup can will need more paper for labelling than orange juice can.

Conclusion:

Therefore, we are able to calculate surface area of cans using simple formulae.