To find the volume [tex]\( V \)[/tex] of the shed, we need to use the formula for the volume of a rectangular prism:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
### Step-by-Step Solution:
1. Identify the dimensions:
- Length: [tex]\( 18.25 \)[/tex] feet
- Width: [tex]\( 15 \)[/tex] feet
- Height: [tex]\( 5 \frac{1}{5} \)[/tex] feet
2. Convert the mixed fraction to a decimal:
The height is given as [tex]\( 5 \frac{1}{5} \)[/tex] feet. This can be converted to an improper fraction and then to a decimal:
[tex]\[ 5 \frac{1}{5} = 5 + \frac{1}{5} = 5 + 0.2 = 5.2 \][/tex] feet
3. Calculate the volume:
Use the formula [tex]\( V = \text{length} \times \text{width} \times \text{height} \)[/tex]:
[tex]\[ V = 18.25 \times 15 \times 5.2 \][/tex]
Performing the multiplication step-by-step:
- First, calculate [tex]\( 18.25 \times 15 \)[/tex].
- Then, multiply the result by 5.2.
After calculating above we get that the volume is:
[tex]\[ V = 1423.5 \text{ cubic feet }\][/tex]
Thus, the correct choice is:
[tex]\[ 1423.5 \text{ cubic feet} \][/tex]
