1)how many Meters of wire (diamter=6.304 x10^-3) can produced from from 5.01 lb of a mixture of ore and copper that is 66% copper
d of copper =8.95 g/cm^3
cylinder =pie r^2 H
answer is 8.32 x 10^3m
2) v=4/3pie r^3, r=17.282 mm
my solutions books says this:
4/3 Pie (17.282 m)^3=72.391=72.391 m^3
i got 2.76 x10^-5
For #1, is that diameter m or cm? I can get the answer you show but only if I don't square diameter.
For #2, I don't get either answer. The book solution seems to be substituting meters instead of mm but even the math is wrong. If you change 17.282 mm to m that is 0.017282 m so
V =(4/3) pi*r^3 = 3.14(0.017282)^3 = 2.16 x 10^-5 m^3.
BTW, that is pi and not pie.
To find the answer to the first question, we need to calculate the amount of copper in the 5.01 lb mixture and then determine how many meters of wire can be produced from that amount of copper.
1) Calculate the amount of copper in the mixture:
- The mixture is 66% copper. So, 66% of 5.01 lb is copper.
- Convert 5.01 lb to grams: 1 lb = 453.6 g, so 5.01 lb = 5.01 lb * 453.6 g/lb = 2269.936 g.
- Determine the amount of copper in grams: 66% of 2269.936 g = 0.66 * 2269.936 g = 1496.96 g.
2) Calculate the volume of the copper:
- Convert the diameter to cm: 6.304 x 10^-3 m = 6.304 x 10^-3 m * 100 cm/m = 0.6304 cm.
- Calculate the radius: radius = diameter/2 = 0.6304 cm / 2 = 0.3152 cm.
- Calculate the volume of the wire using the cylinder formula: volume = π * radius^2 * height. We don't know the height, so let's call it 'h'.
- From the given information, it is not clear what the height of the wire would be, so we cannot find the exact amount of wire that can be produced. However, we can calculate the volume of the wire using the given diameter and radius.
3) Calculate the amount of wire that can be produced:
- Convert the density of copper to g/cm^3: 8.95 g/cm^3.
- Divide the mass of copper by the density to find the volume: volume = mass/density = 1496.96 g / 8.95 g/cm^3.
- This gives us the volume of copper in cm^3.
4) Convert the volume of copper to meters:
- As we found the volume in cm^3, we need to convert it to m^3. 1 cm^3 = 1 x 10^-6 m^3.
- Multiply the volume of copper in cm^3 by the conversion factor to get the volume in m^3.
The final answer for the first question is given as 8.32 x 10^3 m. However, without the height of the wire, it is not possible to determine exactly how many meters of wire can be produced.
For the second question:
From the given formula, v = 4/3πr^3, we need to substitute the given value of r to find the volume.
1) Calculate the volume:
- Plug in the value of r: v = 4/3π(17.282 mm)^3.
- Convert the radius from mm to meters: 17.282 mm = 17.282 mm * 0.001 m/mm = 0.017282 m.
- Substitute the value of r into the formula: v = 4/3 * π * (0.017282 m)^3.
The answer given by your solution book is 72.391 m^3. However, the value you calculated, 2.76 x 10^-5, seems incorrect. Please ensure that you correctly substituted the values and performed the calculations accurately.