To find the surface area of a rectangular tank without a top cover, we can find the area of all six sides and then subtract the area of the top.
The formula for the surface area \(S\) of a rectangular prism is given by:
\[ S = 2(lw + lh + wh) \]
Where:
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.
However, since we are not including the top, we modify our formula to only include the area of the bottom and the four walls.
Given dimensions:
- Length \(l = 33.93\) inches
- Width \(w = 15.81\) inches
- Height \(h = 17.69\) inches
Step 1: Calculate the areas of the sides and the bottom.
Bottom Area:
\[ \text{Area}_{\text{bottom}} = l \times w = 33.93 \times 15.81 \]
Calculating this gives: \[ \text{Area}_{\text{bottom}} \approx 537.0833 \text{ in}^2 \]
Areas of the walls:
-
Two side walls (length times height): \[ \text{Area}{\text{side walls}} = 2 \times (l \times h) = 2 \times (33.93 \times 17.69) \] Calculating this gives: \[ \text{Area}{\text{side walls}} \approx 2 \times 599.1757 \approx 1198.3514 \text{ in}^2 \]
-
Two front and back walls (width times height): \[ \text{Area}{\text{front and back walls}} = 2 \times (w \times h) = 2 \times (15.81 \times 17.69) \] Calculating this gives: \[ \text{Area}{\text{front and back walls}} \approx 2 \times 279.8189 \approx 559.6378 \text{ in}^2 \]
Step 2: Total Surface Area calculation
Now we can add up all the areas: \[ S = \text{Area}{\text{bottom}} + \text{Area}{\text{side walls}} + \text{Area}_{\text{front and back walls}} \] \[ S \approx 537.0833 + 1198.3514 + 559.6378 \approx 2295.0725 \text{ in}^2 \]
Step 3: Round to the nearest hundredth
\[ \text{Surface Area} \approx 2295.07 \text{ in}^2 \]
Conclusion
Looking at the provided options, the closest one is: 2,296.23 in²