Rhodium metal currently costs $1251. per troy ounce (note this is different than a regular ounce! 1 troy ounce = 31.1035g). What would the cost be in dollars to purchase enough gold to form a solid square based pyramid with base dimensions 0.750m by 0.750m and height of 0.500m?
Do you want gold or rhodium? I'm confused by the problem.
I am too, gold, I think. thanks sooo much for your help
For Au. I would change the dimensions to cm so the volume comes out in cc.
volume square based pyramid is
V = (1/3)*(b^2)*h = ?cc
Look up the density of Au in g/cc and
mass Au = density Au x volume from above.
Using the conversion from grams to troy oz, convert to troy oz, then
cost/troy oz x #troy oz = cost of the pyramid in Au. But I wonder what's the point of all of the information on Rh.
To calculate the cost of purchasing enough rhodium to form a solid square-based pyramid, we first need to determine the volume of the pyramid. The volume of a pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
In this case, the base dimensions of the pyramid are given as 0.750m by 0.750m, and the height is 0.500m. We can plug these values into the formula to find the volume of the pyramid.
Base area = 0.750m * 0.750m = 0.5625 square meters
Volume = (1/3) * 0.5625 square meters * 0.500m
= 0.09375 cubic meters
Next, we need to convert the volume of the pyramid from cubic meters to cubic troy ounces. Given that 1 troy ounce is equal to 31.1035 grams, we can convert the volume as follows:
Volume (cubic troy ounces) = Volume (cubic meters) * (1,000,000 grams / 31.1035 grams) * (1 troy ounce / 31.1035 grams)
Now we can calculate the volume in cubic troy ounces:
Volume (cubic troy ounces) = 0.09375 cubic meters * (1,000,000 grams / 31.1035 grams) * (1 troy ounce / 31.1035 grams)
≈ 30.1585 cubic troy ounces
Finally, we can calculate the cost of purchasing the rhodium by multiplying the volume (in troy ounces) by the cost per troy ounce:
Cost = Volume (cubic troy ounces) * Cost per troy ounce
Given the cost of rhodium is $1251 per troy ounce, we can calculate the cost as:
Cost = 30.1585 cubic troy ounces * $1251 per troy ounce
≈ $37,744.07
Therefore, the cost in dollars to purchase enough rhodium to form a solid square-based pyramid with base dimensions 0.750m by 0.750m and a height of 0.500m would be approximately $37,744.07.