To find the volume of the metal piece shaped like an L formed by two rectangular prisms, we can separately calculate the volumes of the two prisms and then add them together.
Dimensions of the longer part of the L (Prism 1):
- Length (L1) = 30 mm
- Width (W1) = 8 mm
- Height (H1) = 8 mm
The volume \( V_1 \) of Prism 1 can be calculated using the formula: \[ V_1 = L1 \times W1 \times H1 \] Substituting the dimensions: \[ V_1 = 30 , \text{mm} \times 8 , \text{mm} \times 8 , \text{mm} = 30 \times 64 = 1920 , \text{mm}^3 \]
Dimensions of the shorter part of the L (Prism 2):
- Length (L2) = 10 mm
- Width (W2) = 8 mm
- Height (H2) = 14 mm (this is how far it extends above the longer part)
The volume \( V_2 \) of Prism 2 can be calculated using the same volume formula: \[ V_2 = L2 \times W2 \times H2 \] Substituting the dimensions: \[ V_2 = 10 , \text{mm} \times 8 , \text{mm} \times 14 , \text{mm} = 10 \times 8 \times 14 = 1120 , \text{mm}^3 \]
Total Volume
Now we can find the total volume \( V \) of the metal piece by adding the volumes of both prisms: \[ V = V_1 + V_2 = 1920 , \text{mm}^3 + 1120 , \text{mm}^3 = 3040 , \text{mm}^3 \]
Thus, the volume of the metal piece is: \[ \boxed{3040 , \text{mm}^3} \]
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