To find the surface area of a right circular cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
Given:
- Diameter = 15.5 cm, so the radius \( r = \frac{15.5}{2} = 7.75 \) cm
- Height \( h = 28 \) cm
- Using \( \pi \approx 3.14 \)
Now, we can calculate the surface area:
-
Calculate \( h + r \): \[ h + r = 28 + 7.75 = 35.75 , \text{cm} \]
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Substitute \( r \), \( h \), and \( \pi \) into the surface area formula: \[ \text{Surface Area} = 2 \times 3.14 \times 7.75 \times 35.75 \]
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Calculate \( 2 \times 3.14 = 6.28 \)
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Now multiply by \( r \): \[ 6.28 \times 7.75 = 48.7575 \]
-
Then multiply by \( h + r \): \[ 48.7575 \times 35.75 \approx 1748.03125 \]
Thus, the surface area of the cylinder is approximately \( 1748.03 , \text{cm}^2 \).
Looking at the provided options, it appears that the closest match is:
1,739.95 cm²
So the final answer is 1,739.95 cm².