To calculate the total surface area and volume of the solid object, we first need to determine the shape of the object based on the provided dimensions \( 8.81' \) and \( 16.2' \). Assuming it is a rectangular prism, let's denote the height as \( h = 8.81' \) and the length as \( l = 16.2' \). However, to calculate the surface area and volume, we also need the width or depth.
Assuming the object is a rectangular prism with an unknown width \( w \). Let's denote:
- \( h = 8.81' \) (height)
- \( l = 16.2' \) (length)
- \( w \) (width)
1. Volume \( V \) of the rectangular prism:
The formula for volume is: \[ V = l \times w \times h \]
2. Total Surface Area \( A \) of the rectangular prism:
The formula for surface area is: \[ A = 2(lw + lh + wh) \] Where:
- \( lw \) = area of the base,
- \( lh \) = area of the front and back,
- \( wh \) = area of the sides.
Example Calculation with a Specific Width:
For a specific width, let's assume \( w = 10' \) as an example to demonstrate the calculations.
Volume Calculation:
\[ V = 16.2' \times 10' \times 8.81' = 1427.622 \text{ cubic feet} \]
Surface Area Calculation:
\[ A = 2(16.2' \cdot 10' + 16.2' \cdot 8.81' + 10' \cdot 8.81') \] Calculating each term:
- \( 16.2 \times 10 = 162 \)
- \( 16.2 \times 8.81 = 142.662 \)
- \( 10 \times 8.81 = 88.1 \)
Now, summing these: \[ 162 + 142.662 + 88.1 = 392.762 \]
Now, multiplying by 2 for the total surface area: \[ A = 2 \times 392.762 = 785.524 \text{ square feet} \]
Final Rounded Results:
- Volume \( V \approx 1427.622 \) cubic feet \( \approx 1420 \) ft³ (to three significant digits).
- Total Surface Area \( A \approx 785.524 \) square feet \( \approx 786 \) ft² (to three significant digits).
Conclusion:
To provide you with the exact surface area and volume, the width \( w \) should be specified, or if the shape is different, let me know the specifics! If the shape is a cylinder or another form, the formulas will differ.