SOLUTION: a pipe is 300cm long it has an internal diameter of 10cm and has a tkickness of 1cm a)find its outer surface area b)its mass if the pipe weghs 3g percm cubes

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Question 261201: a pipe is 300cm long it has an internal diameter of 10cm and has a tkickness of 1cm
a)find its outer surface area
b)its mass if the pipe weghs 3g percm cubes
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
a) A pipe is a cylinder with open ends. For a cylinder the surface area formula is:
SA(cylinder) = 2pi%2Arh+%2B+2pi%2Ar%5E2
Since the 2pi%2Ar%5E2 at the end represents the area of the ends of the cylinder and since we have open ends on the pipe, the formula we will use will leave out that term:
SA(pipe) = 2pi%2Arh

If the inner diameter of the pipe is 10cm then the inner radius is 5cm. With a thickness of 1cm that makes the radius from the center to the outer surface 5+1 or 6 cm. So the surface area is:
SA(pipe) = 2pi%2A%286%29%28300%29
which simplifies to:
SA(pipe) = 3600picm%5E2
This is the exact surface area. If you want a decimal approximation for an answer then substitute a decimal for pi and multiply it by 3600.

b) Since we are given the density (mass per volume) of 3g%2Fcm%5E3, we will be able to figure out the mass if we can figure out the volume. However, since the empty space inside the pipe does not could toward the mass of the pipe, we are not talking about the volume of the open-ended cylinder. We are talking about the volume of the actual physical pipe.

There is no formula for volume (that I know of) of the physical pipe. In situations like this, we need to find some combination of shapes with known formulas for volume which make the shape we have. In this case we have two cylinders:
  • The cylinder of empty space inside the pipe, and
  • The cylinder made up of the empty space plus the physical pipe.

The volume of the physical pipe is the volume of the second cylinder minus the volume of the first (empty) cylinder. Since the volume of a cylinder is:
V(cylinder) = pi%2Ar%5E2h
The volume of the empty space cylinder will be:
V(empty) = pi%2A%285%29%5E2%28300%29+=+7500pi
The volume of the empty space plus the pipe cylinder will be:
V(empty+pipe) = pi%2A%286%29%5E2%28300%29+=+10800pi
So the volume of the pipe is:
V(pipe) = V(empty+pipe) - V(empty) = 10800pi+-+7500pi+=+3300picm%5E3

Now that we know the volume of the pipe we can find the mass. Mass equals density times volume:
M+=+%283g%2Fcm%5E3%293300picm%5E3+=+9900pi g.
Again, this is the exact answer. If you need a decimal approximation, then replace pi with a decimal and multiply by 3300.