An Artisan has 63 kg of metal of density 7,000kg/m3. He intends to use make a rectangular pipe with external dimensions 12 cm by 15 cm and internal dimensions 10 cm by 12 cm. Calculate the length of the pipe in meters.
Volume=63kg ÷ 7000kg/m^3
=0.009m^3
Cross section Area = (12×15)-(10×12)=60cm
60cm^2=0.006m^2
0.009m^3÷0.006m^2= 1.5m
Answer =1.5metres
the cross-section of the pipe is a rectangular ring with area
A = (12*15)-(10*12) = 60 cm^2
so, if the pipe has length x meters, its volume is (60/100)^2*x = 36x/100 m^3
since mass = density * volume, we have
7000*36x/100 = 63
x = 63/2520 = 1/40 m
On my side I speculate, the question was supposed to have asked the volume of the material required to make the pipe,
That is you have to find difference in cross-sections multiplied by the height.
Why do we subtract 180 and 120 to find the product of width and height ?
To calculate the length of the pipe, we need to find the volume of the metal that the Artisan has and then calculate the volume of the pipe.
1. Calculate the volume of the metal available:
Volume = Mass / Density
Given mass of the metal = 63 kg
Density of the metal = 7,000 kg/m^3
Volume = 63 kg / 7,000 kg/m^3
2. Calculate the volume of the pipe:
The external dimensions of the pipe are 12 cm by 15 cm, which is 0.12 m by 0.15 m (convert cm to m).
The internal dimensions of the pipe are 10 cm by 12 cm, which is 0.10 m by 0.12 m.
Subtract the internal dimensions from the external dimensions to get the thickness of the pipe: 0.02 m by 0.03 m.
Volume of the pipe = Length × Width × Thickness
We need to find the length, so rearrange the formula:
Length = Volume of the pipe / (Width × Thickness)
3. Calculate the volume of the pipe:
Volume of the pipe = Volume of the metal available (calculated earlier)
4. Calculate the length of the pipe:
Length = Volume of the pipe / (Width × Thickness)
Substitute the values from step 2 and step 3 into the formula and calculate the length.
By following these steps, you can calculate the length of the pipe.