To calculate the volumes of the larger and smaller prisms, we'll first assume the dimensions given (5 ft, 5 ft, 5 ft, 1.5 ft, 2 ft) pertain to two separate prisms.
Larger Prism
Let's say the larger prism has dimensions:
- Height = 5 ft
- Width = 5 ft
- Length = 5 ft
The volume \( V \) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] So for the larger prism: \[ V = 5 , \text{ft} \times 5 , \text{ft} \times 5 , \text{ft} = 125 , \text{cubic feet} \]
Smaller Prism
Now, let's assume the smaller prism has dimensions:
- Height = 1.5 ft
- Width = 2 ft
- Length = 5 ft
Using the volume formula again for the smaller prism: \[ V = 5 , \text{ft} \times 2 , \text{ft} \times 1.5 , \text{ft} = 15 , \text{cubic feet} \]
Total Volume
The total volume of the figure is the sum of the volumes of the two prisms: \[ \text{Total Volume} = \text{Volume of Larger Prism} + \text{Volume of Smaller Prism} \] \[ \text{Total Volume} = 125 , \text{cubic feet} + 15 , \text{cubic feet} = 140 , \text{cubic feet} \]
Summary of Answers:
- Volume of the larger prism: 125 cubic feet
- Volume of the smaller prism: 15 cubic feet
- Total volume of the figure: 140 cubic feet