To find the volume of the figure made up of two rectangular prisms, we need to calculate the volume of each prism separately and then add them together.
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Volume of the larger rectangular prism:
- Length = 19 feet
- Width = 12 feet
- Height = 6 feet
Volume of a rectangular prism is calculated using the formula: \[ V = \text{Length} \times \text{Width} \times \text{Height} \] Substituting the dimensions of the larger prism: \[ V = 19 \times 12 \times 6 \] \[ V = 228 \times 6 = 1368 \text{ ft}^3 \]
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Volume of the smaller rectangular prism:
- Length = 10 feet
- Width = 12 feet (same as the larger prism since they share the same width)
- Height = 3 feet
Using the same volume formula for the smaller prism: \[ V = \text{Length} \times \text{Width} \times \text{Height} \] Substituting the dimensions of the smaller prism: \[ V = 10 \times 12 \times 3 \] \[ V = 120 \times 3 = 360 \text{ ft}^3 \]
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Total volume of the figure: Now, we add the volumes of both prisms: \[ \text{Total Volume} = \text{Volume of larger prism} + \text{Volume of smaller prism} \] \[ \text{Total Volume} = 1368 + 360 = 1728 \text{ ft}^3 \]
Thus, the total volume of the figure is: \[ \boxed{1728} \text{ ft}^3 \]
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