Question

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

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

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

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

5,040 in.3

Answer 1

To calculate the volume of the desk, we first need to find the volume of the entire desk and then subtract the volumes of the gaps (if any) created by the legs.

1. **Volume of the entire desk:**
- The overall dimensions are:
- Length = 40 inches
- Width = 12 inches
- Height = 24 inches
- Volume = Length × Width × Height
\[
V_{\text{desk}} = 40 \, \text{in} \times 12 \, \text{in} \times 24 \, \text{in} = 11,520 \, \text{in}^3
\]

2. **Volume of the two legs:**
- Each leg has the following dimensions:
- Width = 10 inches
- Depth = 12 inches (assuming the depth is the same as the width of the desk)
- Height = 18 inches
- Volume of one leg = Width × Depth × Height
\[
V_{\text{leg}} = 10 \, \text{in} \times 12 \, \text{in} \times 18 \, \text{in} = 2,160 \, \text{in}^3
\]
- Since there are two legs:
\[
V_{\text{total legs}} = 2 \times 2,160 \, \text{in}^3 = 4,320 \, \text{in}^3
\]

3. **Final volume of the desk:**
- Subtract the volume of the legs from the volume of the overall desk:
\[
V_{\text{desk}} = 11,520 \, \text{in}^3 - 4,320 \, \text{in}^3 = 7,200 \, \text{in}^3
\]

Thus, the volume of the desk is **7,200 in³**.

The correct response is:
**7,200 in³**