To find the lateral surface area of a cylinder, we can use the formula:
\[ \text{Lateral Surface Area} = 2\pi rh \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
From the dimensions provided in your question, it appears that the height (h) of the cylinder is 3 cm. However, the width (9 cm) doesn't directly indicate the radius of a circular base.
If we interpret the width as the diameter of the cylinder, we can find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{9 , \text{cm}}{2} = 4.5 , \text{cm} \]
Now we can substitute the radius and height into the lateral surface area formula:
\[ \text{Lateral Surface Area} = 2\pi (4.5 , \text{cm})(3 , \text{cm}) \]
Calculating the surface area:
\[ \text{Lateral Surface Area} = 2\pi (13.5 , \text{cm}^2) \] \[ \text{Lateral Surface Area} = 27\pi , \text{cm}^2 \] \[ \text{Lateral Surface Area} \approx 27 \times 3.14 \approx 84.78 , \text{cm}^2 \]
None of the options you provided match this calculation. However, if the interpretation of the dimensions differs (like the height being width or diameter), please clarify or check the values again. Based on the given dimensions and using 9 cm as the diameter of the base of the cylinder, the calculated lateral surface area is approximately \( 84.78 , \text{cm}^2 \).