To find the total surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Height \( h = 2 \)
- Radius \( r = 3 \)
Now, plug in the values:
-
Calculate the area of the two circular bases: \[ 2\pi r^2 = 2\pi (3^2) = 2\pi (9) = 18\pi \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2\pi (3)(2) = 12\pi \]
-
Add both areas to find the total surface area: \[ \text{Total Surface Area} = 18\pi + 12\pi = 30\pi \]
Now calculate \( 30\pi \) using \( \pi \approx 3.14 \):
\[ 30\pi \approx 30 \times 3.14 = 942 \]
Thus, the total surface area rounded to the nearest hundredth is approximately
\[ \boxed{94.20} \]