To find the surface area of a rectangular tank without a top cover, we can use the formula for the surface area of a rectangular prism, which is:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height. Since the tank does not have a top, we will modify the formula to exclude the top area:
\[ \text{Surface Area (without top)} = lw + 2lh + 2wh \]
Given dimensions:
- Length (\( l \)) = 33.93 inches
- Width (\( w \)) = 15.81 inches
- Height (\( h \)) = 17.69 inches
Calculate each component:
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Calculate \( lw \): \[ lw = 33.93 \times 15.81 = 536.0023 \text{ in}^2 \]
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Calculate \( 2lh \): \[ 2lh = 2 \times 33.93 \times 17.69 = 2 \times 599.1767 = 1198.3534 \text{ in}^2 \]
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Calculate \( 2wh \): \[ 2wh = 2 \times 15.81 \times 17.69 = 2 \times 279.0649 = 558.1298 \text{ in}^2 \]
Now, add them:
\[ \text{Surface Area} = lw + 2lh + 2wh = 536.0023 + 1198.3534 + 558.1298 \]
Calculating this gives: \[ \text{Surface Area} = 2292.4855 \text{ in}^2 \]
Rounding to the nearest hundredth:
The surface area of the turtle's tank, not including a top cover, is approximately: \[ \text{Surface Area} \approx 2292.49 \text{ in}^2 \]
Checking the options:
Among the given responses, the one that is the closest to our calculated value (2292.49) is 2,296.23 in².
So, the final answer is: 2,296.23 in².