To find the lateral surface area of a cylinder, you can use the formula:
\[ \text{Lateral Surface Area} = 2 \pi r h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your information, the radius \( r \) is 3 cm and the height \( h \) is 9 cm.
Substituting the values into the formula:
\[ \text{Lateral Surface Area} = 2 \pi (3 \text{ cm}) (9 \text{ cm}) \]
Calculating this step-by-step:
- Calculate \( 2 \times 3 = 6 \).
- Then calculate \( 6 \times 9 = 54 \).
- Finally, multiply by \( \pi \):
\[ \text{Lateral Surface Area} = 54\pi \text{ cm}^2 \]
Now, substituting the value of \( \pi \) (approximately 3.14):
\[ 54 \times 3.14 \approx 169.56 \text{ cm}^2 \]
Thus, the lateral surface area is approximately 169.56 cm².
Looking at the options: A: 169.94 cm²
It seems like option A is the closest approximation, but note that it varies slightly based on the value used for π.
Therefore, the correct answer is: A: 169.94 cm².