Thank you for visiting A soup can has a height of 4 inches and a radius of 2 5 inches What s 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 :
To find the area of paper needed to cover the lateral face of a soup can with a label, we need to calculate the lateral surface area of the can. The can has a cylindrical shape, and its lateral surface area can be determined using the formula for the lateral surface area of a cylinder, which is:
[tex]\[ \text{Lateral Surface Area} = 2 \pi r h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
- [tex]\( \pi \)[/tex] is approximately 3.14159
Given:
- The radius of the can [tex]\( r = 2.5 \)[/tex] inches
- The height of the can [tex]\( h = 4 \)[/tex] inches
Let's plug these values into the formula:
1. Calculate the circumference of the base (which is part of the lateral surface formula):
[tex]\[ \text{Circumference} = 2 \pi r = 2 \times 3.14159 \times 2.5 \][/tex]
2. Use this circumference to find the lateral surface area:
[tex]\[ \text{Lateral Surface Area} = \text{Circumference} \times h = (2 \times 3.14159 \times 2.5) \times 4 \][/tex]
3. Performing the calculations gives:
[tex]\[ \text{Lateral Surface Area} \approx 62.8 \][/tex]
Therefore, the area of paper needed to cover the lateral face of the soup can with a label is approximately [tex]\( 62.8 \, \text{in}^2 \)[/tex].
The correct answer is:
C) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
[tex]\[ \text{Lateral Surface Area} = 2 \pi r h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
- [tex]\( \pi \)[/tex] is approximately 3.14159
Given:
- The radius of the can [tex]\( r = 2.5 \)[/tex] inches
- The height of the can [tex]\( h = 4 \)[/tex] inches
Let's plug these values into the formula:
1. Calculate the circumference of the base (which is part of the lateral surface formula):
[tex]\[ \text{Circumference} = 2 \pi r = 2 \times 3.14159 \times 2.5 \][/tex]
2. Use this circumference to find the lateral surface area:
[tex]\[ \text{Lateral Surface Area} = \text{Circumference} \times h = (2 \times 3.14159 \times 2.5) \times 4 \][/tex]
3. Performing the calculations gives:
[tex]\[ \text{Lateral Surface Area} \approx 62.8 \][/tex]
Therefore, the area of paper needed to cover the lateral face of the soup can with a label is approximately [tex]\( 62.8 \, \text{in}^2 \)[/tex].
The correct answer is:
C) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
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Rewritten by : Jeany
