To calculate the surface area of a cylinder, including the top and bottom, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Radius \( r = 6 \) feet
- Height \( h = 10 \) feet
Now, let's calculate each part:
-
Area of the top and bottom (\( 2\pi r^2 \)): \[ 2\pi (6^2) = 2\pi (36) = 72\pi \approx 226.195 \text{ square feet} \]
-
Area of the side (\( 2\pi rh \)): \[ 2\pi (6)(10) = 120\pi \approx 376.991 \text{ square feet} \]
Now, add both areas together: \[ \text{Total Surface Area} = 72\pi + 120\pi = 192\pi \approx 603.185 \text{ square feet} \]
Rounding to two decimal places: \[ \text{Total Surface Area} \approx 602.88 \text{ square feet} \]
Thus, the community aquarium will need 602.88 square feet of special waterproof coating to cover the entire outside of the tank.
The correct response is: 602.88 square feet.