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the top of the cylinder is 2cm and the round part is 5cm
Question
Find the surface area of a cylinder. Use 3.14 for π
.
Round your answer to the nearest tenths place.
(1 point)
Responses
87.9 cm2
87.9 cm 2
175.8 cm2
175.8 cm 2
120.3 cm2
120.3 cm 2
75.3 cm2
the top of the cylinder is 2cm and the round part is 5cm
Question
Find the surface area of a cylinder. Use 3.14 for π
.
Round your answer to the nearest tenths place.
(1 point)
Responses
87.9 cm2
87.9 cm 2
175.8 cm2
175.8 cm 2
120.3 cm2
120.3 cm 2
75.3 cm2
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the surface area of a cylinder, we can use the formula:
\[
SA = 2\pi r(h + r)
\]
Where:
- \(SA\) is the surface area,
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder,
- \(\pi\) is approximately 3.14.
From your question:
- The diameter of the top of the cylinder is given as 2 cm, which means the radius \(r\) is \( \frac{2}{2} = 1 \) cm.
- The height \(h\) of the cylinder is given as 5 cm.
Now we can substitute the values into the formula:
\[
SA = 2 \cdot 3.14 \cdot 1 \cdot (5 + 1)
\]
Calculating it step-by-step:
1. Calculate \(h + r\):
\[
h + r = 5 + 1 = 6
\]
2. Calculate \(2 \cdot 3.14 \cdot 1 \cdot 6\):
\[
SA = 2 \cdot 3.14 \cdot 6 = 2 \cdot 18.84 = 37.68
\]
3. Finally, round \(37.68\) to the nearest tenths place, which remains \(37.7\) cm².
This surface area doesn't match any options you provided. Let's check the calculations once more for any mistakes.
Using the surface area formula again:
- The cylinder has a top and bottom (2 circles), and the curved surface area.
- The correct formula for the total surface area of a cylinder is:
\[
SA = 2\pi r^2 + 2\pi rh
\]
Calculating the area again:
1. Area of the two circles:
\[
2\pi r^2 = 2 \cdot 3.14 \cdot (1)^2 = 2 \cdot 3.14 \cdot 1 = 6.28
\]
2. Area of the curved surface:
\[
2\pi rh = 2 \cdot 3.14 \cdot 1 \cdot 5 = 2 \cdot 3.14 \cdot 5 = 31.4
\]
Adding these two areas together:
\[
SA = 6.28 + 31.4 = 37.68
\]
Upon double-checking the calculations for potential misinterpretations or data entry errors, it seems the values used may not align perfectly with your options.
To clarify, it seems that there may be a miscommunication regarding either the dimensions or the selections you provided, which typically would lead to results around the \(37.68\) cm² area.
If we adjust cylinder parameters or if any details were omitted, please provide those for a reevaluation. I hope this clears up the surface area computation!
\[
SA = 2\pi r(h + r)
\]
Where:
- \(SA\) is the surface area,
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder,
- \(\pi\) is approximately 3.14.
From your question:
- The diameter of the top of the cylinder is given as 2 cm, which means the radius \(r\) is \( \frac{2}{2} = 1 \) cm.
- The height \(h\) of the cylinder is given as 5 cm.
Now we can substitute the values into the formula:
\[
SA = 2 \cdot 3.14 \cdot 1 \cdot (5 + 1)
\]
Calculating it step-by-step:
1. Calculate \(h + r\):
\[
h + r = 5 + 1 = 6
\]
2. Calculate \(2 \cdot 3.14 \cdot 1 \cdot 6\):
\[
SA = 2 \cdot 3.14 \cdot 6 = 2 \cdot 18.84 = 37.68
\]
3. Finally, round \(37.68\) to the nearest tenths place, which remains \(37.7\) cm².
This surface area doesn't match any options you provided. Let's check the calculations once more for any mistakes.
Using the surface area formula again:
- The cylinder has a top and bottom (2 circles), and the curved surface area.
- The correct formula for the total surface area of a cylinder is:
\[
SA = 2\pi r^2 + 2\pi rh
\]
Calculating the area again:
1. Area of the two circles:
\[
2\pi r^2 = 2 \cdot 3.14 \cdot (1)^2 = 2 \cdot 3.14 \cdot 1 = 6.28
\]
2. Area of the curved surface:
\[
2\pi rh = 2 \cdot 3.14 \cdot 1 \cdot 5 = 2 \cdot 3.14 \cdot 5 = 31.4
\]
Adding these two areas together:
\[
SA = 6.28 + 31.4 = 37.68
\]
Upon double-checking the calculations for potential misinterpretations or data entry errors, it seems the values used may not align perfectly with your options.
To clarify, it seems that there may be a miscommunication regarding either the dimensions or the selections you provided, which typically would lead to results around the \(37.68\) cm² area.
If we adjust cylinder parameters or if any details were omitted, please provide those for a reevaluation. I hope this clears up the surface area computation!
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