<PRE><B>Question 261201</B>
a) A pipe is a cylinder with open ends. For a cylinder the surface area formula is:
SA(cylinder) = {{{2pi*rh + 2pi*r^2}}}
Since the {{{2pi*r^2}}} 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*rh}}}&lt;br&gt;
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*(6)(300)}}}
which simplifies to:
SA(pipe) = {{{3600pi}}}{{{cm^2}}}
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.&lt;br&gt;
b) Since we are given the density (mass per volume) of {{{3g/cm^3}}}, 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.&lt;br&gt;
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:&lt;ul&gt;&lt;li&gt;The cylinder of empty space inside the pipe, and&lt;/li&gt;&lt;li&gt;The cylinder made up of the empty space plus the physical pipe.&lt;/li&gt;&lt;/ul&gt;
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*r^2h}}}
The volume of the empty space cylinder will be:
V(empty) = {{{pi*(5)^2(300) = 7500pi}}}
The volume of the empty space plus the pipe cylinder will be:
V(empty+pipe) = {{{pi*(6)^2(300) = 10800pi}}}
So the volume of the pipe is:
V(pipe) = V(empty+pipe) - V(empty) = {{{10800pi - 7500pi = 3300pi}}}{{{cm^3}}}&lt;br&gt;
Now that we know the volume of the pipe we can find the mass. Mass equals density times volume:
{{{M = (3g/cm^3)3300pi}}}{{{cm^3 = 9900pi}}} g.
Again, this is the exact answer. If you need a decimal approximation, then replace pi with a decimal and multiply by 3300.</PRE>