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: \[ V = \text{Base Area} \times \text{Height} \]
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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: \[ A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 , \text{m} \times 3.5 , \text{m} = 3.5 , \text{m}^2. \]
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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: \[ \boxed{28 , \text{m}^3}. \]
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