Question

This diagram shows the dimensions of a metal piece used in a machine.

What is the volume of the metal piece?

Enter your answer in the box.

mm³
Three-dimensional figure that could be formed by placing two rectangular prisms together to form a sideways L shape where the longer part of the L is on the bottom and the shorter part of the L extends up from the right side. The longer part of the L has a length of 30 millimeters, a width of 8 millimeters, and a height of 8 millimeters. The shorter part of the L extends 14 millimeters above the longer part of the L and has a length of 10 millimeters.

Answer 1

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:
\[
\boxed{3040 \, \text{mm}^3}
\]