To calculate the density of the tube, we need to know its mass and volume. We are given the mass of the tube as 6.5 grams. To find the volume, we can use the formula for the volume of a cylinder: $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.

First, we need to convert the diameter to radius by dividing it by 2:

$r = 0.8 \text{ inches} / 2 = 0.4 \text{ inches}$

Next, we need to convert the height to meters, since the density should be in SI units:

$h = 10.6 \text{ cm} \times 10^{-2} \text{ m/cm} = 0.106 \text{ m}$

Finally, we can convert the radius to meters:

$r = 0.4 \text{ inches} \times 2.54 \text{ cm/inch} \times 10^{-2} \text{ m/cm} = 0.1016 \text{ m}$

Now we can calculate the volume:

$V = \pi r^2 h = \pi \cdot (0.1016 \text{ m})^2 \cdot (0.106 \text{ m}) = 3.49 \times 10^{-5} \text{ m}^3$

And finally, we can calculate the density:

$\rho = \frac{m}{V} = \frac{6.5 \text{ g}}{3.49 \times 10^{-5} \text{ m}^3} = 1852 \text{ kg/m}^3$

So the density of the tube is approximately 1852 kilograms per cubic meter.
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