An open pit mine is being dug in the Buffalo Ridge mountain range. It will be 550 feet across and 290 feet deep. Based on sampling of the area, experts project that the company will be able to retrieve an average of about 0.115 ounces of gold per ton of ore and waste mined. The mine company estimates the total cost of production will be $80 million. (Assume the shape of the pit is a perfect cone.) (a) What would be the volume of ore and waste material removed during its mining operation? (b) How many ounces of gold should the company expect to recover from this mine? (Assume one ton is equal to 10 cubic feet.)

Question

Mathematics

Jeffrey

23 August, 09:48

An open pit mine is being dug in the Buffalo Ridge mountain range. It will be 550 feet across and 290 feet deep. Based on sampling of the area, experts project that the company will be able to retrieve an average of about 0.115 ounces of gold per ton of ore and waste mined. The mine company estimates the total cost of production will be $80 million. (Assume the shape of the pit is a perfect cone.) (a) What would be the volume of ore and waste material removed during its mining operation? (b) How many ounces of gold should the company expect to recover from this mine? (Assume one ton is equal to 10 cubic feet.)

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Simon Spence · Answer 1

The formula for volume of a cone is:

V = PI x r^2 x h/3

r = radius = 550 / 2 = 275

h = 290

Find the volume:

A) Volume = 3.14 x 275^2 x 290/3 = 22,954,708 cubic feet.

Now convert to tons and then multiply by ounces per ton of gold.

B) 22,954,708 / 10 = 22,95,470.8 tons

22,95,470.8 x 0.115 = 263,979 ounces of gold.