To calculate the volume of the desk, we need to account for the volume of the entire rectangular shape and then subtract the volume of the gaps created by the legs.
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Volume of the entire desk:
- Length = 40 inches
- Width = 12 inches
- Height = 24 inches
\[ \text{Volume}{\text{desk}} = \text{Length} \times \text{Width} \times \text{Height} = 40 \times 12 \times 24 \] \[ \text{Volume}{\text{desk}} = 11520 \text{ in}^3 \]
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Volume of each leg:
- Width of each leg = 10 inches
- Height of each leg = 18 inches
- Depth of each leg = 12 inches (the width of the desk)
\[ \text{Volume}{\text{leg}} = \text{Width} \times \text{Height} \times \text{Depth} = 10 \times 18 \times 12 \] \[ \text{Volume}{\text{leg}} = 2160 \text{ in}^3 \]
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Volume of both legs:
- Since there are two legs: \[ \text{Volume}{\text{legs}} = 2 \times \text{Volume}{\text{leg}} = 2 \times 2160 = 4320 \text{ in}^3 \]
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Volume of the desk without the legs:
- Now subtract the volume of the legs from the volume of the desk: \[ \text{Volume}{\text{desk without legs}} = \text{Volume}{\text{desk}} - \text{Volume}{\text{legs}} = 11520 - 4320 \] \[ \text{Volume}{\text{desk without legs}} = 7200 \text{ in}^3 \]
Thus, the total volume of the desk after accounting for the space taken by the legs is 7200 cubic inches.
The answer is:
7,200 in³.