Question

A community aquarium is building a new cylinder shaped fish tank for their tropical fish exhibit. The tank needs to have a radius of 6 feet and a height of 10 feet. How much surface area of special waterproof coating will they need to cover the entire outside of the tank, including the top and bottom?(1 point)
Responses

414.48 square feet
414.48 square feet

672 square feet
672 square feet

602.88 square feet
602.88 square feet

804 square feet
804 square feet

1 answer

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:

  1. Area of the top and bottom (\( 2\pi r^2 \)): \[ 2\pi (6^2) = 2\pi (36) = 72\pi \approx 226.195 \text{ square feet} \]

  2. 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.