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Question

An illustration shows a drawing of a pedestal desk with two full-width legs and a gap in the middle. The overall length of the table is 40 inches, the overall width is 12 inches, and the overall height is 24 inches. The two legs on the sides are each 10 inches wide and 18 inches high.

What is the volume of the desk?

(1 point)
Responses

8,640 in.3
8,640 in. cubed

5,040 in.3
5,040 in. cubed

5,760 in.3
5,760 in. cubed

7,200 in.3
7,200 in. cubed
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Answer 1

To find the volume of the desk, we need to calculate the volume of the entire rectangular structure first and then subtract the volume of the legs.

1. Volume of the desk:

   • The desk is in the shape of a rectangular prism.
   • Volume = Length × Width × Height
   • Given: Length = 40 inches, Width = 12 inches, Height = 24 inches

   Volume of the desk = 40 in × 12 in × 24 in = 11,520 in³

2. Volume of the two legs:

   • Each leg is also a rectangular prism.
   • Volume of one leg = Width × Depth × Height
   • Each leg has: Width = 10 inches, Depth = (Assuming depth equal to desk's width = 12 inches), Height = 18 inches

   Volume of one leg = 10 in × 12 in × 18 in = 2,160 in³ Since there are two legs, we multiply this by 2:

   Volume of two legs = 2 × 2,160 in³ = 4,320 in³

3. Volume of the desk structure (excluding legs):

   • Subtract the volume of the legs from the total volume of the desk.

   Volume of desk structure = Volume of desk - Volume of two legs Volume of desk structure = 11,520 in³ - 4,320 in³ = 7,200 in³

So the volume of the desk is 7,200 in³.

The correct response is 7,200 in.³.