To calculate the volume of this trapezoidal prism (pile of crushed stone, "tas de concassé"):

Trapezoidal Prism Volume Formula

The volume $V$ of a trapezoidal prism can be calculated using: $V = A_b \times h$ where:

• $A_b$ = Area of the trapezoidal base.
• $h$ = Height (thickness) of the prism.

Step 1: Calculate the Area of the Trapezoidal Base

The formula for the area of a trapezoid is: $A_b = \frac{1}{2} \times (B_1 + B_2) \times h_t$ where:

• $B_1 = 100"$ (larger base),
• $B_2 = 50"$ (smaller base),
• $h_t = 30.25"$ (height of the trapezoid).

Plugging in the values: $A_b = \frac{1}{2} \times (100 + 50) \times 30.25$ $A_b = \frac{1}{2} \times 150 \times 30.25 = 2268.75 \, \text{in}^2$

Step 2: Calculate the Volume

The height $h$ of the prism is given as $30"$.

Using: $V = A_b \times h$ $V = 2268.75 \times 30 = 68062.5 \, \text{in}^3$

Final Volume

The volume of the trapezoidal prism is approximately: $68,062.5 \, \text{in}^3$

Would you like a conversion to cubic feet or a detailed explanation of the steps? Let me know!

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5 Related Questions:

1. How can the volume be converted from cubic inches to cubic feet?
2. What is the significance of the trapezoid's height in calculating volume?
3. How can you calculate the surface area of this prism?
4. What other shapes could approximate the volume of this object for quick calculations?
5. How do real-world factors like compaction affect these calculations?

Tip:

Always double-check measurements and units when performing volume calculations, especially in mixed-unit systems!