A cylindrical pipe 2 ½ metres long has an internal diameter of 21 millimetres and an external diameter of 35 millimetres. The density of the material that makes the pipe is 1.25 g/cm‘. Calculate the mass of the pipe in kilograms. (Take n = 22/7)
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To calculate the mass of the pipe, we need to find the volume of the material it is made of and then multiply it by the density.
First, let's calculate the volume of the material inside the pipe:
1. Find the inner radius (r1) of the pipe:
The internal diameter is given as 21 millimetres. The radius can be calculated as half of the diameter:
r1 = 21/2 = 10.5 millimetres = 10.5/10 = 1.05 centimetres
2. Find the outer radius (r2) of the pipe:
The external diameter is given as 35 millimetres. The radius can be calculated as half of the diameter:
r2 = 35/2 = 17.5 millimetres = 17.5/10 = 1.75 centimetres
3. Calculate the volume of the material using the formula for the volume of a pipe:
V = π * (r2^2 - r1^2) * h,
where π is Pi (approximately 22/7), r2 is the outer radius, r1 is the inner radius, and h is the height of the pipe.
In this case, the height (h) of the pipe is given as 2 ½ meters, which can be calculated as 2.5 meters.
V = (22/7) * ((1.75)^2 - (1.05)^2) * 2.5 cubic centimeters
Now, let's calculate the mass of the pipe:
4. Multiply the volume by the density:
The density of the material is given as 1.25 g/cm³.
Mass = V * density
Mass = [(22/7) * ((1.75)^2 - (1.05)^2) * 2.5] * 1.25 grams
5. Convert the mass from grams to kilograms by dividing by 1000:
Mass(kg) = Mass(g) / 1000
So, the final answer will be the mass of the pipe in kilograms.