Use the image to answer the question.

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

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

7,200 in.3
7,200 in. cubed

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

Answer 1

To find the volume of the desk, we calculate the volume of the entire rectangular prism that makes up the top of the desk and subtract the volume of the legs.

1. Calculate the volume of the whole desk (rectangular prism):

   • Length = 40 inches
   • Width = 12 inches
   • Height = 24 inches

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

2. Calculate the volume of one leg:

   • Each leg is a rectangular prism with:
     • Width = 10 inches
     • Depth = (assuming it has the same height as the overall height of the desk) = 12 inches (same as the overall width)
     • Height = 18 inches

   Volume of one leg = Width × Depth × Height
   Volume = 10 in × 12 in × 18 in = 2,160 in³

3. Calculate the total volume of the two legs: Volume of two legs = 2 × Volume of one leg
   Volume of two legs = 2 × 2,160 in³ = 4,320 in³

4. Find the volume of the desk without the legs: Volume of the desk without the legs = Total volume of the desk - Total volume of the legs
   Volume = 11,520 in³ - 4,320 in³ = 7,200 in³

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

The correct response is: 7,200 in.³.