To find the volume of the solid rectangular prism with a hole, we will first calculate the volume of the outer solid prism and then subtract the volume of the inner hole.
- Volume of the outer solid prism:
The formula for the volume of a rectangular prism is given by: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
For the outer solid prism:
- Length = 15 mm
- Width = 6 mm
- Height = 6 mm
Calculating the volume: \[ \text{Volume}_{\text{outer}} = 15 , \text{mm} \times 6 , \text{mm} \times 6 , \text{mm} = 540 , \text{mm}^3 \]
- Volume of the hole (inner prism):
Using the same formula for the volume of the rectangular prism for the hole:
- Length = 15 mm
- Width = 4 mm
- Height = 4 mm
Calculating the volume of the hole: \[ \text{Volume}_{\text{hole}} = 15 , \text{mm} \times 4 , \text{mm} \times 4 , \text{mm} = 240 , \text{mm}^3 \]
- Volume of the solid with the hole:
Now, subtract the volume of the hole from the volume of the outer prism: \[ \text{Volume}{\text{solid}} = \text{Volume}{\text{outer}} - \text{Volume}{\text{hole}} \] \[ \text{Volume}{\text{solid}} = 540 , \text{mm}^3 - 240 , \text{mm}^3 = 300 , \text{mm}^3 \]
Thus, the volume of the solid rectangular prism with the hole is: \[ \boxed{300} , \text{mm}^3 \]