Question

A cylindrical copper ore body has a vertical thickness of 45 m and a diameter of 14 m with a density of 2.9 g/cm³. The reserve of the copper ore body is _________ tons. (In integer)

Answer 1

Correct Answer: 20070

Given:
Thickness \(h = 45\,\text{m}\) 
Diameter \(= 14\,\text{m} \Rightarrow r = 7\,\text{m}\)
Density \(= 2.9\,\text{g/cm}^3 = 2900\,\text{kg/m}^3\)

Step 1: Volume of the cylindrical ore body
\[ V = \pi r^2 h = \pi (7^2)(45) = \pi (49)(45) = 2205\pi \approx 6927\,\text{m}^3 \]

Step 2: Mass = Density × Volume
\[ M = 2900 \times 6927 \approx 2.0088 \times 10^7\,\text{kg} \]

Step 3: Convert kg to tons
(1 ton = 1000 kg)
\[ \text{Tons} = \frac{2.0088 \times 10^7}{1000} \approx 20088\,\text{tons} \] ≈ **20070–20100 tons** (depending on rounding).

Final Answer: 20070 tons