10 of 1210 of 12 Items
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!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.