To calculate the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
From your description, the cylinder has a height of 13 and a diameter of 5. This means the radius \( r \) is half of the diameter:
\[ r = \frac{5}{2} = 2.5 \]
Now, plug the values into the surface area formula:
- Calculate \( h + r \):
\[ h + r = 13 + 2.5 = 15.5 \]
- Calculate the surface area:
\[ \text{Surface Area} = 2 \times 3.14 \times 2.5 \times 15.5 \]
Now, performing the calculations:
\[ 2 \times 3.14 = 6.28 \]
Then, calculate \( 6.28 \times 2.5 \):
\[ 6.28 \times 2.5 = 15.7 \]
Now, multiply by \( 15.5 \):
\[ 15.7 \times 15.5 = 243.35 \]
Finally, the total surface area is:
\[ \text{Surface Area} \approx 243.35 \]
It seems that the available options do not match, so I will double-check the calculations.
Calculating using the complete formula again gives us:
\[ \text{Surface Area} = 2\pi r(h + r) = 2 \times 3.14 \times 2.5 \times 15.5 = 245.82 \]
This also does not match your responses. Assuming these are misalignments in the options provided, none of the options seem to correctly reflect the surface area calculation using the provided dimensions of the cylinder.
Please check the options provided again to clarify.