Questions: The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.

Solution Steps

The dimensions of the outer rectangular prism are 15 mm (length) x 6 mm (width) x 6 mm (height).

\[ \text{Volume}_{\text{outer}} = \text{length} \times \text{width} \times \text{height} \] \[ \text{Volume}_{\text{outer}} = 15 \, \text{mm} \times 6 \, \text{mm} \times 6 \, \text{mm} \] \[ \text{Volume}_{\text{outer}} = 540 \, \text{mm}^3 \]

The dimensions of the inner rectangular prism (hole) are 15 mm (length) x 4 mm (width) x 4 mm (height).

\[ \text{Volume}_{\text{inner}} = \text{length} \times \text{width} \times \text{height} \] \[ \text{Volume}_{\text{inner}} = 15 \, \text{mm} \times 4 \, \text{mm} \times 4 \, \text{mm} \] \[ \text{Volume}_{\text{inner}} = 240 \, \text{mm}^3 \]

To find the volume of the solid, subtract the volume of the inner rectangular prism from the volume of the outer rectangular prism.

\[ \text{Volume}_{\text{solid}} = \text{Volume}_{\text{outer}} - \text{Volume}_{\text{inner}} \] \[ \text{Volume}_{\text{solid}} = 540 \, \text{mm}^3 - 240 \, \text{mm}^3 \] \[ \text{Volume}_{\text{solid}} = 300 \, \text{mm}^3 \]

Final Answer