Chapter 12.9, Problem 4GP

To determine

To check: Whether more paper is required to label a can of orange juice than a soup can.

Answer to Problem 4GP

More paper needed to make the label of the can of soup in comparison to the can of orange juice.

Explanation of Solution

Given information:

The height of the can of orange juice is 5 inches and diameter $2\frac{1}{2}$ inches. The height of the can of soup is $5.5$ inches and radius 2 inches.

Calculation:

The larger lateral surface area results in more paper needed.

Write the expression to calculate the lateral area of the can of orange juice.

  $\text{Lateral}{\text{area}}_{\text{orange}}=2\pi rh$

Where,

• $r$ is the radius of the can of orange juice.
• $h$ is the height of the can of orange juice.

Substitute the values in the above expression.

  $\begin{array}{c}\text{Lateral}{\text{area}}_{\text{orange}}=2\pi \left(\frac{2\frac{1}{2}}{2}\right)5\\ =39.3{\text{in}}^2\end{array}$

Write the expression to calculate the lateral area of the can of orange juice.

  $\text{Lateral}{\text{area}}_{\text{soup}}=2\pi r_1{h}_1$

Where,

• $r_1$ is the radius of the can of soup.
• $h_1$ is the height of the can of soup.

Substitute the values in the above expression.

  $\begin{array}{c}\text{Lateral}{\text{area}}_{\text{soup}}=2\pi \times 2\times 5.5\\ =69.1{\text{in}}^2\end{array}$

From the above, it is clear that the lateral surface area of the can of soup is more than the lateral surface area of the can of orange juice. Hence, more paper needed to make the label of the can of soup.

Conclusion:

Therefore, more paper needed to make the label of the can of soup in comparison to the can of orange juice.