To calculate the total surface area of a cylinder, we need to find the lateral surface area and the area of the two circular bases.
The formulas we need are:
- Lateral Surface Area (LSA) = \( 2\pi rh \)
- Area of the two bases = \( 2\pi r^2 \)
Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately 3.14159
Given:
- Height \( h = 2 \) ft
- Radius \( r = 3 \) ft
Step 1: Calculate the Lateral Surface Area
\[ \text{LSA} = 2\pi rh = 2\pi(3)(2) = 12\pi \approx 12 \times 3.14159 \approx 37.69908 \text{ ft}^2 \]
Step 2: Calculate the Area of the Two Bases
\[ \text{Area of the bases} = 2\pi r^2 = 2\pi(3^2) = 2\pi(9) = 18\pi \approx 18 \times 3.14159 \approx 56.54867 \text{ ft}^2 \]
Step 3: Calculate the Total Surface Area
\[ \text{Total Surface Area} = \text{LSA} + \text{Area of the bases} = 12\pi + 18\pi = 30\pi \approx 30 \times 3.14159 \approx 94.24778 \text{ ft}^2 \]
Step 4: Round to the Nearest Hundredth
\[ \text{Total Surface Area} \approx 94.25 \text{ ft}^2 \]
Therefore, the total surface area of the cylinder is approximately 94.25 ft².