Question

Question 7: Consider the figure. 30 in, 30 in, 2 in, 25 in, 4 in, 12 in, 12 in, 8 in, 8 in
Determine the volume of the top of the table ____ cubic inches
Determine the volume of the leg of the table _____ cubic inches
Determine the volume of the base of the table _____ cubic inches
Determine the total volume of the table _____ cubic inches

Answer 1

To determine the volume of the various parts of the table, we first need to clarify the measurements and the shapes we are dealing with. Assuming this is a standard table with a rectangular top, cylindrical legs, and a base, here’s how to calculate the volume for each component based on the given dimensions. However, please note I will make some assumptions since I don't have the figure itself.

### Assumptions:
- The top of the table is a rectangular prism.
- The legs are cylindrical.
- There is a base that could either be a rectangular prism or another cylindrical shape.

### Given Dimensions:
- Top of the table: 30 in by 30 in (assuming square)
- Thickness of the top: 2 in
- Legs of the table: 25 in (height) and 4 in (diameter)
Let's assume the legs are cylindrical.
- Base of the table: 12 in by 12 in (assuming square) and 8 in height.

### Calculations:

1. **Volume of the top of the table (V_top)**:
- Formula for the volume of a rectangular prism: \( V = \text{length} \times \text{width} \times \text{height} \)
- Here, length = 30 in, width = 30 in, height = 2 in.
\[
V_{\text{top}} = 30 \, \text{in} \times 30 \, \text{in} \times 2 \, \text{in} = 1800 \, \text{cubic inches}
\]

2. **Volume of one leg of the table (V_leg)**:
- For cylindrical legs, the formula is: \( V = \pi r^2 h \)
- Diameter = 4 in, so radius \( r = \frac{4}{2} = 2 \, \text{in} \)
- Height = 25 in.
\[
V_{\text{leg}} = \pi (2 \, \text{in})^2 (25 \, \text{in}) = \pi \cdot 4 \cdot 25 \approx 314.16 \, \text{cubic inches}
\]
- There are 4 legs, so total volume for legs:
\[
V_{\text{legs}} = 4 \times 314.16 \approx 1256.64 \, \text{cubic inches}
\]

3. **Volume of the base of the table (V_base)**:
- Assuming it's also a rectangular prism: dimensions = 12 in by 12 in by 8 in.
\[
V_{\text{base}} = 12 \, \text{in} \times 12 \, \text{in} \times 8 \, \text{in} = 1152 \, \text{cubic inches}
\]

4. **Total volume of the table (V_total)**:
- Total volume combines the top, legs, and base:
\[
V_{\text{total}} = V_{\text{top}} + V_{\text{legs}} + V_{\text{base}} = 1800 + 1256.64 + 1152 = 3208.64 \, \text{cubic inches}
\]

### Summary:
- Volume of the top of the table: **1800 cubic inches**
- Volume of the legs of the table: **1256.64 cubic inches** (for 4 legs)
- Volume of the base of the table: **1152 cubic inches**
- Total volume of the table: **3208.64 cubic inches**

Please verify the dimensions and assumptions to ensure accurate calculations based on your specific figure.