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

1 answer

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.