To find the surface area of the right circular cylinder, we can use the formula for the surface area \( A \):
\[ A = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Height \( h = 28 \) cm,
- Diameter = 15.5 cm, so the radius \( r = \frac{15.5}{2} = 7.75 \) cm.
Now, substituting the values into the surface area formula:
\[ A = 2 \cdot 3.14 \cdot 7.75 \cdot (28 + 7.75) \]
First, calculate \( 28 + 7.75 \):
\[ 28 + 7.75 = 35.75 \]
Now substitute that back into the formula:
\[ A = 2 \cdot 3.14 \cdot 7.75 \cdot 35.75 \]
Now, calculate it step by step:
- Calculate \( 2 \cdot 3.14 = 6.28 \).
- Calculate \( 7.75 \cdot 35.75 \):
\[ 7.75 \cdot 35.75 = 277.5625 \]
- Now multiply:
\[ A = 6.28 \cdot 277.5625 \]
Calculating that:
\[ A \approx 1740.045 , \text{cm}^2 \]
Rounding to two decimal places, we get:
\[ A \approx 1740.05 , \text{cm}^2 \]
Looking at the answers provided, the closest option is:
1,739.95 cm²
So, the answer is:
1,739.95 cm²