Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![**Cylinder Label Surface Area Calculation**
A company makes paper labels for paint cans. As illustrated below, each can is shaped like a cylinder with a height of 6 inches and a radius of 4 inches. The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company makes 13 labels, how many square inches of paper will be needed? Use 3.14 for π, and do not round your answer.
**Diagram**
- It shows a cylinder with a height of 6 inches and a radius of 4 inches.
**Formula**
To determine the surface area of the label, calculate the lateral surface area of the cylinder using the formula:
\[ \text{Lateral Surface Area} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height.
**Calculation Steps**
1. Identify the radius \( r = 4 \) inches and the height \( h = 6 \) inches.
2. Substitute the values and use \( \pi = 3.14 \) into the formula:
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 4 \times 6 \]
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 24 \]
\[ \text{Lateral Surface Area} = 150.72 \text{ square inches} \]
To find the total paper required for 13 labels:
\[ \text{Total Paper Needed} = 13 \times 150.72 \]
\[ \text{Total Paper Needed} = 1959.36 \text{ square inches} \]
Thus, the company will need 1959.36 square inches of paper to make 13 labels.
**Submission**
\( \boxed{1959.36} \)
**User Interface Description**
- Diagram: A cylinder is displayed with the dimensions annotated.
- Text Entry: A space to input the calculated area.
- Buttons: Include calculation functions (e.g., \( \times \)), a reset button, and a submit button.
- Links: Privacy and Terms of Use are present along with an accessibility option.
**Educational Notes**
- This exercise helps students practice geometric calculations, specifically the surface area of a cylinder.
- Emphasizes the real-world application of these math concepts in manufacturing and labeling processes.](https://content.bartleby.com/qna-images/question/a73137ae-240e-4c93-bec2-8644cade406a/630afe05-3536-4279-b0ef-d9999cac5284/nvx18td_processed.jpeg)
Transcribed Image Text:**Cylinder Label Surface Area Calculation**
A company makes paper labels for paint cans. As illustrated below, each can is shaped like a cylinder with a height of 6 inches and a radius of 4 inches. The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company makes 13 labels, how many square inches of paper will be needed? Use 3.14 for π, and do not round your answer.
**Diagram**
- It shows a cylinder with a height of 6 inches and a radius of 4 inches.
**Formula**
To determine the surface area of the label, calculate the lateral surface area of the cylinder using the formula:
\[ \text{Lateral Surface Area} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height.
**Calculation Steps**
1. Identify the radius \( r = 4 \) inches and the height \( h = 6 \) inches.
2. Substitute the values and use \( \pi = 3.14 \) into the formula:
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 4 \times 6 \]
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 24 \]
\[ \text{Lateral Surface Area} = 150.72 \text{ square inches} \]
To find the total paper required for 13 labels:
\[ \text{Total Paper Needed} = 13 \times 150.72 \]
\[ \text{Total Paper Needed} = 1959.36 \text{ square inches} \]
Thus, the company will need 1959.36 square inches of paper to make 13 labels.
**Submission**
\( \boxed{1959.36} \)
**User Interface Description**
- Diagram: A cylinder is displayed with the dimensions annotated.
- Text Entry: A space to input the calculated area.
- Buttons: Include calculation functions (e.g., \( \times \)), a reset button, and a submit button.
- Links: Privacy and Terms of Use are present along with an accessibility option.
**Educational Notes**
- This exercise helps students practice geometric calculations, specifically the surface area of a cylinder.
- Emphasizes the real-world application of these math concepts in manufacturing and labeling processes.
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