Volume of Composite 3D Figures Quick Check
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Question
Use the image to answer the 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
5,040 in.3
5,040 in. cubed
5,760 in.3
5,760 in. cubed
8,640 in.3
8,640 in. cubed
7,200 in.3
wrong
To find the volume of the desk, we first find the volume of the rectangular prism part of the desk. This can be found by multiplying the overall length, width, and height of the desk:
Volume = 40 in x 12 in x 24 in
Volume = 11,520 in³
Next, we subtract the volume of the two legs on the sides. To find the volume of one leg, we multiply the width, height, and depth (which is the overall width for the legs) of the leg and then multiply by 2 for both legs:
Volume of one leg = 10 in x 18 in x 12 in = 2,160 in³
Volume of both legs = 2 x 2,160 in³ = 4,320 in³
Finally, we subtract the volume of the legs from the volume of the desk to find the volume of the remaining structure:
Volume of desk = 11,520 in³ - 4,320 in³ = 7,200 in³
Therefore, the volume of the desk is 7,200 in.³.
I apologize for the error. Let's correct that.
To find the volume of the desk, we first find the volume of the rectangular prism part of the desk, which is the overall length x overall width x overall height:
Volume of rectangular prism = 40 in x 12 in x 24 in = 11,520 in³
Next, we find the volume of the two legs on the sides. The volume of each leg is width x height x depth (overall width for legs) and then multiplied by 2 for both legs:
Volume of one leg = 10 in x 18 in x 12 in = 2,160 in³
Volume of both legs = 2 x 2,160 in³ = 4,320 in³
Finally, we subtract the volume of the legs from the volume of the desk to find the volume of the remaining structure:
Volume of desk = 11,520 in³ - 4,320 in³ = 7,200 in³
Therefore, the correct volume of the desk is **7,200 in.³**. Thank you for your patience.