To find the volume of the rectangular prism, we use the formula for the volume \( V \) of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given dimensions:
- Height (\( h \)) = 1012 in.
- Length (\( l \)) = 623 in.
- Width (\( w \)) = 214 in.
Now we can calculate the volume:
\[ V = 623 , \text{in.} \times 214 , \text{in.} \times 1012 , \text{in.} \]
Calculating step-by-step:
- Calculate \( 623 \times 214 = 133282 \) in².
- Multiply by the height: \( 133282 \times 1012 \).
Performing that final multiplication:
\[ 133282 \times 1012 = 134707824 , \text{in}^3 \]
Now, let's compare this volume to the volume of the item:
The item has dimensions:
- Height = 8 in.
- Length = 6 in.
- Width = 2 in.
Calculating the volume of the item:
\[ V_{\text{item}} = 6 , \text{in.} \times 2 , \text{in.} \times 8 , \text{in.} = 96 , \text{in}^3 \]
Now, we see that \( 134707824 , \text{in}^3 \) (volume of the prism) is much larger than \( 96 , \text{in}^3 \) (volume of the item). Therefore, the item should fit inside the prism.
Final answer choice is:
15712 in.³ and yes, the item should fit inside the prism.
(Note: Please verify the calculation as I initially stated \( 134707824 , \text{in}^3 \), which seems different from the options you provided. It appears there may be discrepancies in the provided answer choices.)