Question 6: Consider this figure, 5 ft, 5 ft, 5 ft, 1.5 ft, 2 ft

Determine the volume of the larger prism. _____ cubic feet
Determine the volume of the smaller prism. _____ cubic feet
Determine the total volume of the figure. ______ cubic feet

1 answer

To determine the volumes of the prism, we need to identify the shapes and their dimensions based on the provided measurements.

Volume of the Larger Prism

Assuming the larger prism is a rectangular prism with a base measuring 5 ft by 5 ft and a height of 2 ft:

\[ \text{Volume of larger prism} = \text{Base Area} \times \text{Height} = (5 , \text{ft} \times 5 , \text{ft}) \times 2 , \text{ft} \] \[ \text{Volume of larger prism} = 25 , \text{ft}^2 \times 2 , \text{ft} = 50 , \text{cubic feet} \]

Volume of the Smaller Prism

Assuming the smaller prism has the same base dimensions (5 ft by 5 ft) but a height of 1.5 ft:

\[ \text{Volume of smaller prism} = \text{Base Area} \times \text{Height} = (5 , \text{ft} \times 5 , \text{ft}) \times 1.5 , \text{ft} \] \[ \text{Volume of smaller prism} = 25 , \text{ft}^2 \times 1.5 , \text{ft} = 37.5 , \text{cubic feet} \]

Total Volume of the Figure

To find the total volume, we sum the volumes of both prisms:

\[ \text{Total Volume} = \text{Volume of larger prism} + \text{Volume of smaller prism} \] \[ \text{Total Volume} = 50 , \text{cubic feet} + 37.5 , \text{cubic feet} = 87.5 , \text{cubic feet} \]

Summary of the Volumes

  • Volume of the larger prism: 50 cubic feet
  • Volume of the smaller prism: 37.5 cubic feet
  • Total volume of the figure: 87.5 cubic feet