Question

The area of a triangular block of a massive orebody is $1500 m^2$. If the thickness of the orebody is 5 m, 6 m and 7 m at the three corners of the triangular block, and the ore density is $2.5 tons/m^3$, the estimated ore reserve of the block is ______ tons. (In integer)

Answer 1

Correct Answer: 22500

Estimating the Ore Reserve of a Triangular Block 

Step 1: Calculate the Average Thickness

The average thickness can be calculated using the formula:

\[ \text{Average thickness} = \frac{5 + 6 + 7}{3} = 6 \, \text{m} \]

Step 2: Calculate the Volume of the Orebody

The volume of the orebody is calculated by multiplying the area by the average thickness:

\[ \text{Volume} = \text{Area} \times \text{Average thickness} = 1500 \, \text{m}^2 \times 6 \, \text{m} = 9000 \, \text{m}^3 \]

Step 3: Calculate the Ore Reserve

The ore reserve is then calculated by multiplying the volume by the ore density:

\[ \text{Ore reserve} = \text{Volume} \times \text{Ore density} = 9000 \, \text{m}^3 \times 2.5 \, \text{tons/m}^3 = 22500 \, \text{tons} \]

Final Answer:

The estimated ore reserve of the block is: 22500 tons.