i don't understand

Question

The cylinder can be made from steel. The top will be open and the thickness of the steel will be 0.5ft thick, making up the walls and the bottom. Steel can be purchased for $0.29 per kilogram and has a density of 7.95g/cm³. What is the cost of the steel to the nearest dollar?

Btw the surface area of the cylinder is 3456π ft² and the volume is 26973π ft³

Answer 1

Hi Mindy,

Having thought about this a bit, I realize there is another method to get the answer that has a couple of fewer steps. The key is still to get the radius and height of the cylinder as described before. The next step would be to calculate the void volume of the cylinder, the empty space inside, and subtract that from the total volume. What is left is the steel shell of the cylinder. To do that, once you have the radius and height of the cylinder, calculate the void volume using the formula V = hπr² because the void volume is also a cylinder. For the dimensions of the void cylinder, use the dimensions of the shell minus 0.5 ft which is the thickness of the cylinder. So you formula would be V_void = (h_shell -0.5) x π(r_shell - 0.5)².Subtracting that value from the given volume of the cylinder gives you the volume of steel, then use the conversion factors to determine the price.

Hope that helps.

Answer 2

Make sure the surface area given (3456π ft²) is the sides and the bottom. If it is, then here goes:

Multiply the surface area by the steel thickness to give you the volume of the steel needed (in cubic feet). Note that you do NOT use the volume of the cylinder in this calculation.

So (3456π ft²)(0.5 ft) = 5428.6721 ft³

Now you must convert it to a mass so that you can apply the price ($0.29/kg) to it. You do that by multiplying the volume by the density. But the density they gave you is in the wrong units (volume is in cubic feet and the density is in g/cm³). If you multiply density in g/cm³ by 1000 it will turn into density in kg/m³. So the density is 7950 kg/m³.

But now you must convert your volume to cubic meters. You can do that by multiplying volume in ft³ by 0.028317 so (5428.6721)(0.028317) = 153.723 m³

Now multiply the volume by the density:

(153.723 m³)(7950 kg/m³) = 1,222,097 kg

Now multiply the mass by the cost/mass so:

(1,222,097 kg)($0.29 /kg) = $354,408.09