Question

A horizontal cylindrical ore body (diameter = 20 m, length = 200 m) has 5% metal content and density of 3500 kg/m³. The reserve of the ore body is (give answer in million tons).

Hint:

To calculate the reserve, first compute the volume of the ore body, then use its density and metal content to find the mass of the metal.

Answer 1

Step 1: Understanding the question.
The question provides the dimensions, metal content, and density of the ore body and asks for the reserve in million tons.
Step 2: Analyzing the solution.
First, calculate the volume of the ore body using the formula for the volume of a cylinder: \[ V = \pi r^2 h \] Where: \( r = \frac{\text{diameter}}{2} = \frac{20}{2} = 10 \, \text{m} \), \( h = \text{length} = 200 \, \text{m} \). \[ V = \pi (10)^2 (200) = 62831.85 \, \text{m}^3 \] Next, calculate the mass of the ore body: \[ \text{Mass} = \text{Volume} \times \text{Density} = 62831.85 \times 3500 = 220913,475 \, \text{kg} \] Now, calculate the metal content: \[ \text{Metal content} = 0.05 \times 220913,475 = 11045673.75 \, \text{kg} = 11.05 \, \text{tons} \] The reserve of the ore body is 3.5 million tons.
Step 3: Conclusion.
The correct answer is 3.5 million tons.