To calculate the volume of the pedestal desk, we can break it down into two parts: the volume of the top surface of the desk and the volume of the two side legs.
1. Volume of the top:
The top of the desk can be considered as a rectangular box with a length of 40 inches, a width of 12 inches, and a height (or thickness) that is typically small for a desk but isn't provided in the question. For the sake of this calculation, if we assume the desk top is 1 inch thick (a common approximation), we can calculate its volume as follows:
\[ \text{Volume}_{\text{top}} = \text{length} \times \text{width} \times \text{height} \]
\[ \text{Volume}_{\text{top}} = 40 , \text{in} \times 12 , \text{in} \times 1 , \text{in} = 480 , \text{in}^3 \]
2. Volume of the two legs:
Each leg of the desk is 10 inches wide, 18 inches high, and we can assume the depth is the same as the width of the top, which is 12 inches. Therefore, the volume of one leg is given by:
\[ \text{Volume}_{\text{leg}} = \text{width} \times \text{height} \times \text{depth} \]
\[ \text{Volume}_{\text{leg}} = 10 , \text{in} \times 18 , \text{in} \times 12 , \text{in} = 2160 , \text{in}^3 \]
Since there are two legs, we multiply this by 2:
\[ \text{Total Volume}_{\text{legs}} = 2 \times 2160 , \text{in}^3 = 4320 , \text{in}^3 \]
3. Total Volume of the desk:
Now we add the volume of the top and the total volume of the legs:
\[ \text{Total Volume}{\text{desk}} = \text{Volume}{\text{top}} + \text{Total Volume}_{\text{legs}} \]
\[ \text{Total Volume}_{\text{desk}} = 480 , \text{in}^3 + 4320 , \text{in}^3 = 4800 , \text{in}^3 \]
However, the result of \(4800 , \text{in}^3\) does not match any of the given options. Given the options provided, it seems they are much larger than our calculated final volume, which suggests our assumptions or calculations regarding either the height/thickness of the top or the dimensions of the legs might differ significantly from typical values.
On revising calculations and assumptions properly regarding what the desk's total dimensions usually include, please reconsider if any part of the desk wasn't factored in or if any dimension should imply a typical thickness that hasn't been specified which could contribute to a larger calculation value.
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