To find the total surface area of a cylinder, you can use the formula:
\[ \text{Total Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately \( 3.14 \).
You mentioned that the area is 3 ft, but to calculate the total surface area of the cylinder, we need to clarify that the area mentioned isn't directly related to \( r \) or \( h \). Given that height \( h = 2 \) ft, we will first need to find the radius \( r \) using the provided area, which we will assume is the area of the base of the cylinder.
The area of the base of the cylinder (which is a circle) is given by the formula:
\[ \text{Area of base} = \pi r^2 \]
Since you mentioned the area is 3 ft², we set this equal to the area of the base:
\[ \pi r^2 = 3 \]
To find \( r \):
\[ r^2 = \frac{3}{\pi} \approx \frac{3}{3.14} \approx 0.955 \] \[ r \approx \sqrt{0.955} \approx 0.977 \text{ ft} \]
Now we can substitute \( r \) and \( h \) back into the total surface area formula:
- Calculate \( 2\pi r^2 \):
\[ 2\pi r^2 = 2 \pi (0.977)^2 \approx 2 \pi (0.955) \approx 2 \cdot 3.14 \cdot 0.955 \approx 6.0 \text{ ft}^2 \]
- Calculate \( 2\pi rh \):
\[ 2\pi rh = 2 \pi (0.977)(2) \approx 4 \pi (0.977) \approx 4 \cdot 3.14 \cdot 0.977 \approx 12.16 \text{ ft}^2 \]
- Now sum those results to find the total surface area:
\[ \text{Total Surface Area} \approx 6.0 + 12.16 \approx 18.16 \text{ ft}^2 \]
Finally, we round this to the nearest hundredth:
\[ \text{Total Surface Area} \approx 18.16 \text{ ft}^2 \]
Thus, the total surface area of the cylinder, rounded to the nearest hundredth, is 18.16 ft².