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 (the side) of the soup can, we need to calculate the lateral surface area of the cylinder-shaped can.
First, recall the formula for the lateral surface area of a cylinder:
[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] (pi) is a constant approximately equal to 3.14159.
Given:
- The height [tex]\( h \)[/tex] of the soup can is 4 inches,
- The radius [tex]\( r \)[/tex] of the soup can is 2.5 inches.
Plug these values into the formula:
[tex]\[ \text{Lateral Surface Area} = 2 \pi (2.5) (4) \][/tex]
First, perform the multiplication within the parentheses:
[tex]\[ 2.5 \times 4 = 10 \][/tex]
Next, multiply by 2 and then by [tex]\( \pi \)[/tex]:
[tex]\[ 2 \times 10 = 20 \][/tex]
[tex]\[ 20 \times \pi \approx 20 \times 3.14159 = 62.8318 \][/tex]
Thus, the lateral surface area is approximately:
[tex]\[ 62.8318 \, \text{square inches} \][/tex]
When comparing this result with the given options:
- Option A) [tex]\( 125.7 \, \text{in}^2 \)[/tex]
- Option B) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
- Option C) [tex]\( 78.5 \, \text{in}^2 \)[/tex]
The closest match is:
- Option B) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
Therefore, the area of paper needed to cover the lateral face of the soup can is:
[tex]\[ \boxed{62.8 \, \text{in}^2} \][/tex]
First, recall the formula for the lateral surface area of a cylinder:
[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] (pi) is a constant approximately equal to 3.14159.
Given:
- The height [tex]\( h \)[/tex] of the soup can is 4 inches,
- The radius [tex]\( r \)[/tex] of the soup can is 2.5 inches.
Plug these values into the formula:
[tex]\[ \text{Lateral Surface Area} = 2 \pi (2.5) (4) \][/tex]
First, perform the multiplication within the parentheses:
[tex]\[ 2.5 \times 4 = 10 \][/tex]
Next, multiply by 2 and then by [tex]\( \pi \)[/tex]:
[tex]\[ 2 \times 10 = 20 \][/tex]
[tex]\[ 20 \times \pi \approx 20 \times 3.14159 = 62.8318 \][/tex]
Thus, the lateral surface area is approximately:
[tex]\[ 62.8318 \, \text{square inches} \][/tex]
When comparing this result with the given options:
- Option A) [tex]\( 125.7 \, \text{in}^2 \)[/tex]
- Option B) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
- Option C) [tex]\( 78.5 \, \text{in}^2 \)[/tex]
The closest match is:
- Option B) [tex]\( 62.8 \, \text{in}^2 \)[/tex]
Therefore, the area of paper needed to cover the lateral face of the soup can is:
[tex]\[ \boxed{62.8 \, \text{in}^2} \][/tex]
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Rewritten by : Jeany
