To find the volume of the pedestal desk, we can calculate the volume by treating it as a rectangular prism, then subtracting the volume of the gaps (if necessary).
-
Calculate the overall volume of the desk: \[ \text{Volume of the desk} = \text{Length} \times \text{Width} \times \text{Height} = 40 , \text{in} \times 12 , \text{in} \times 24 , \text{in} = 11,520 , \text{in}^3 \]
-
Calculate the volume of the two legs: Each leg is a rectangular prism with a width of 10 inches, a height of 18 inches, and a depth that we can assume to be the same as the desk's overall width (which is likely a reasonable assumption).
\[ \text{Volume of one leg} = \text{Width} \times \text{Height} \times \text{Depth} = 10 , \text{in} \times 18 , \text{in} \times 12 , \text{in} = 2,160 , \text{in}^3 \]
Since there are two legs: \[ \text{Volume of both legs} = 2 \times 2,160 , \text{in}^3 = 4,320 , \text{in}^3 \]
-
Calculate the final volume of the desk: Now we subtract the volume of the two legs from the overall volume of the desk. \[ \text{Final volume} = \text{Volume of desk} - \text{Volume of legs} = 11,520 , \text{in}^3 - 4,320 , \text{in}^3 = 7,200 , \text{in}^3 \]
Therefore, the volume of the desk is 7,200 in.³.