Volume of Composite Solid Figures - Free Printable

The image shows a composite 3D shape made up of two rectangular prisms (boxes) joined together. We are asked to find the volume of the entire figure.

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Step 1: Understand the Shape

The figure consists of:
- A tall rectangular prism on the left.
- A shorter rectangular prism on the right, attached at the bottom.

Let’s break it down into two separate boxes and compute their volumes individually.

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Step 2: Dimensions of Each Prism

#### Left Prism (Tall One)

- Height = 12 inches (total height of the left side)
- Width = 6 inches (given at the top)
- Depth = 5 inches (same as the depth of the whole figure, given at the bottom)

> Note: The depth is consistent across both parts because they are aligned in the third dimension.

So, volume of left prism:

$$
V_1 = \text{length} \times \text{width} \times \text{height} = 6 \times 5 \times 12 = 360 \text{ in}^3
$$

#### Right Prism (Shorter One)

- Height = 8 inches (given)
- Width = ? Let's find this.

Total width of the whole figure is 14 inches.
The left prism takes up 6 inches of that width.

So, the right prism has width:

$$
14 - 6 = 8 \text{ inches}
$$

Depth = 5 inches (same as before)

So, volume of right prism:

$$
V_2 = 8 \times 5 \times 8 = 320 \text{ in}^3
$$

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Step 3: Total Volume

Add both volumes:

$$
V_{\text{total}} = V_1 + V_2 = 360 + 320 = \boxed{680} \text{ cubic inches}
$$

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✔ Final Answer:

$$
\boxed{680} \text{ in}^3
$$

This is the total volume of the composite solid.