Thank you for visiting A soup can has a height of 4 inches and a radius of 2 5 inches What is the area of paper needed to cover. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's solve this problem together step-by-step to find the area of paper needed to cover the lateral face of a soup can.
### Problem Restatement:
We need to find the area of the label that would cover the lateral surface of a soup can with given dimensions:
- Height (h) = 4 inches
- Radius (r) = 2.5 inches
### Step-by-Step Solution:
1. Understand the formula for the lateral surface area of a cylinder:
The lateral surface area [tex]\( A \)[/tex] of a cylinder can be found using the formula:
[tex]\[
A = 2 \pi r h
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
2. Substitute the given values into the formula:
- Radius [tex]\( r = 2.5 \)[/tex] inches
- Height [tex]\( h = 4 \)[/tex] inches
By substituting these values into the formula, we get:
[tex]\[
A = 2 \pi \times 2.5 \times 4
\][/tex]
3. Perform the calculations:
- Calculate [tex]\( 2 \times 2.5 \)[/tex]:
[tex]\[
2 \times 2.5 = 5
\][/tex]
- Multiply this result by 4:
[tex]\[
5 \times 4 = 20
\][/tex]
- Now, multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[
A = 20 \times \pi = 20 \times 3.14159 \approx 62.832
\][/tex]
### Conclusion:
The calculated lateral surface area is approximately 62.832 square inches. This value closely matches one of the given answer choices.
Therefore, the area of paper needed to cover the lateral face of the soup can is:
[tex]\[ C) \ 62.8 \ \text{in}^2 \][/tex]
This is the correct answer.
### Problem Restatement:
We need to find the area of the label that would cover the lateral surface of a soup can with given dimensions:
- Height (h) = 4 inches
- Radius (r) = 2.5 inches
### Step-by-Step Solution:
1. Understand the formula for the lateral surface area of a cylinder:
The lateral surface area [tex]\( A \)[/tex] of a cylinder can be found using the formula:
[tex]\[
A = 2 \pi r h
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
2. Substitute the given values into the formula:
- Radius [tex]\( r = 2.5 \)[/tex] inches
- Height [tex]\( h = 4 \)[/tex] inches
By substituting these values into the formula, we get:
[tex]\[
A = 2 \pi \times 2.5 \times 4
\][/tex]
3. Perform the calculations:
- Calculate [tex]\( 2 \times 2.5 \)[/tex]:
[tex]\[
2 \times 2.5 = 5
\][/tex]
- Multiply this result by 4:
[tex]\[
5 \times 4 = 20
\][/tex]
- Now, multiply by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[
A = 20 \times \pi = 20 \times 3.14159 \approx 62.832
\][/tex]
### Conclusion:
The calculated lateral surface area is approximately 62.832 square inches. This value closely matches one of the given answer choices.
Therefore, the area of paper needed to cover the lateral face of the soup can is:
[tex]\[ C) \ 62.8 \ \text{in}^2 \][/tex]
This is the correct answer.
Thank you for reading the article A soup can has a height of 4 inches and a radius of 2 5 inches What is the area of paper needed to cover. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
