Question

Jane builds a ramp made of a triangular prism and a rectangular prism. What is the volume of the ramp? 2m, 3.5, 4m, 1m.

Answer 1

To calculate the volume of Jane's ramp made up of a triangular prism and a rectangular prism, we need to know how the dimensions provided (2m, 3.5m, 4m, 1m) correspond to each shape.

### Step 1: Volume of the Triangular Prism
The volume \( V \) of a triangular prism can be calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]

1. **Find the Base Area**:
- The triangular base could have a base of 2m and a height of 3.5m.
- The area \( A \) of the triangle is:
\[
A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \, \text{m} \times 3.5 \, \text{m} = 3.5 \, \text{m}^2.
\]

2. **Height of the prism**:
- Assuming the height (or length) of the triangular prism is 4m.

Putting this together, the volume \( V_t \) of the triangular prism is:
\[
V_t = A \times \text{height} = 3.5 \, \text{m}^2 \times 4 \, \text{m} = 14 \, \text{m}^3.
\]

### Step 2: Volume of the Rectangular Prism
The volume \( V \) of a rectangular prism can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

Assuming the rectangular prism has a length of 4m and a width of 1m, and a height of 3.5m:
\[
V_r = 4 \, \text{m} \times 1 \, \text{m} \times 3.5 \, \text{m} = 14 \, \text{m}^3.
\]

### Step 3: Total Volume of the Ramp
Now, we can find the total volume of the ramp by adding the volumes of both shapes:
\[
V_{\text{total}} = V_t + V_r = 14 \, \text{m}^3 + 14 \, \text{m}^3 = 28 \, \text{m}^3.
\]

Thus, the total volume of Jane's ramp is:
\[
\boxed{28 \, \text{m}^3}.
\]