An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long.

Question

What is the volume of the composite figure?

(1 point)
in.3

Answer 1

To find the volume of the composite figure made up of three rectangular prisms, we will calculate the volume of each individual prism and then sum them up.

1. Volume of the side rectangular prisms: Each side rectangular prism has dimensions:

   • Length = 16 inches
   • Width = 7 inches
   • Height = 7 inches

   The volume \(V\) of a rectangular prism is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]

   For each side prism: \[ V = 16 \times 7 \times 7 = 16 \times 49 = 784 \text{ cubic inches} \]

   Since there are two identical side prisms: \[ \text{Total volume of side prisms} = 2 \times 784 = 1568 \text{ cubic inches} \]

2. Volume of the center rectangular prism: The center rectangular prism has dimensions:

   • Length = 10 inches
   • Width = 8 inches
   • Height = 7 inches (assuming it is the same height as the side prisms)

   For the center prism: \[ V = 10 \times 8 \times 7 = 80 \times 7 = 560 \text{ cubic inches} \]

3. Total volume of the composite figure: Now, we add the volumes of the side prisms and the center prism: \[ \text{Total volume} = \text{Volume of side prisms} + \text{Volume of center prism} \] \[ = 1568 + 560 = 2128 \text{ cubic inches} \]

Thus, the volume of the composite figure is \(\boxed{2128}\) cubic inches.