To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where \( r \) is the radius and \( h \) is the height.
Given that the dimensions are \( 5 \) (assumed to be the diameter) and \( 13 \) (the height), we can first calculate the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5 \]
Now we can substitute the values into the surface area formula. The height \( h \) is \( 13 \).
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 2.5 \cdot (13 + 2.5) \]
Calculate \( h + r \):
\[ h + r = 13 + 2.5 = 15.5 \]
Now substitute \( h + r \) back into the formula:
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 2.5 \cdot 15.5 \]
Now calculate it step by step:
- Calculate \( 2 \cdot 3.14 = 6.28 \)
- Calculate \( 6.28 \cdot 2.5 = 15.7 \)
- Finally, calculate \( 15.7 \cdot 15.5 \):
\[ 15.7 \cdot 15.5 = 243.35 \]
Now remember to multiply the result by \( 1 \) since we are calculating surface area.
The approximate surface area of the cylinder is 243.35 square units.
It seems none of the response options (1469.52, 408.2, 565.2, 204.1) provided match the calculation based on the values given (5 for diameter, 13 for height). Please verify the dimensions or response options again.
1 answer