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:
-
Calculate \(h + r\): \[ h + r = 5 + 1 = 6 \]
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Calculate \(2 \cdot 3.14 \cdot 1 \cdot 6\): \[ SA = 2 \cdot 3.14 \cdot 6 = 2 \cdot 18.84 = 37.68 \]
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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:
-
Area of the two circles: \[ 2\pi r^2 = 2 \cdot 3.14 \cdot (1)^2 = 2 \cdot 3.14 \cdot 1 = 6.28 \]
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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!