To find the surface area of the turtle tank that does not include a top cover, we can use the concept of a net. The tank is a rectangular prism, so we need to find the areas of the bottom and the four sides.
The formula for the surface area \( S \) of a rectangular prism that does not include the top is:
\[ S = (Length \times Width) + (2 \times Height \times Length) + (2 \times Height \times Width) \]
Given dimensions:
- Length \( L = 33.93 \) inches
- Width \( W = 15.81 \) inches
- Height \( H = 17.69 \) inches
Now, we calculate each part of the surface area:
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Area of the bottom: \[ \text{Area of Bottom} = L \times W = 33.93 \times 15.81 \]
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Area of the front and back (two identical rectangles): \[ \text{Area of Front and Back} = 2 \times (H \times L) = 2 \times (17.69 \times 33.93) \]
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Area of the sides (two identical rectangles): \[ \text{Area of Sides} = 2 \times (H \times W) = 2 \times (17.69 \times 15.81) \]
Now we can compute each area:
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Area of the bottom: \[ 33.93 \times 15.81 \approx 536.3353 \text{ in}^2 \]
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Area of the front and back: \[ 2 \times (17.69 \times 33.93) \approx 2 \times 599.9357 \approx 1199.8714 \text{ in}^2 \]
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Area of the sides: \[ 2 \times (17.69 \times 15.81) \approx 2 \times 279.0649 \approx 558.1298 \text{ in}^2 \]
Now, we sum these areas to find the total surface area:
\[ S = 536.3353 + 1199.8714 + 558.1298 \]
Calculating this gives:
\[ S \approx 2294.3365 \text{ in}^2 \]
Rounding to the nearest hundredth, the surface area is:
\[ S \approx 2294.34 \text{ in}^2 \]
None of the provided answers match the exact calculation, but rounding error could be a factor. The closest response is:
2,296.23 in²