Question

Explain how you could get a formula for the volume of the solid.
Find the volume using a combined formula.

13cm
5cm
2cm

Answer 1

To find the volume of a solid using a combined formula, you typically need to identify the shape of the solid and how the dimensions you have correspond to its volume.

### Step 1: Identify the Solid
From the provided dimensions (13 cm, 5 cm, and 2 cm), it's not clear what the shape of the solid is. However, if we assume you are looking for the volume of a rectangular cuboid (a box), then you can use the formula for the volume of a rectangular prism:

**Volume of a Rectangular Prism (Cuboid)**:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

### Step 2: Assign Dimensions
In this case, you can assign:
- Length \( l = 13 \, \text{cm} \)
- Width \( w = 5 \, \text{cm} \)
- Height \( h = 2 \, \text{cm} \)

### Step 3: Calculate the Volume
Using the formula:
\[
V = 13 \, \text{cm} \times 5 \, \text{cm} \times 2 \, \text{cm}
\]
Now calculate:
\[
V = 13 \times 5 = 65 \, \text{cm}^2
\]
Then multiply by height:
\[
65 \, \text{cm}^2 \times 2 \, \text{cm} = 130 \, \text{cm}^3
\]

### Conclusion
The volume of the solid (assumed to be a rectangular cuboid) using the given dimensions is:
\[
V = 130 \, \text{cm}^3
\]

If the solid is actually a different shape, you'll need to adjust your approach based on what that shape is (e.g., cylinder, cone, sphere, etc.). If you provide clarification on what the solid is, I can provide a more precise calculation.