Question

In your first lab, you will measure the diameter and height of a cylinder. The diameter will be measured with a micrometer and the height will be measured with a vernier caliper. Say you measure a diameter of 5.1±0.0005 cm and a height of 37.6±0.005 cm. What will be the uncertainty in your volume?

Answer 1

ΔV = ±0.175 cm

Step-by-step explanation:

The equation for volume is

V = π/4 * d^2 * h

All the measurements are multiplied. To propagate uncertainties in multiplication we add the relative uncertainties together.

The relative uncertainty of the diameter is:

εd = Δd/d

εd = 0.0005/5.1 = 0.000098

The relative uncertainty of the height is:

εh = Δh/h

εh = 0.005/37.6 = 0.00013

Then, the relative uncertainty of the volume is:

εV = 2 * εd + εh

εV = 2 * 0.000098 + 0.00013 = 0.000228

Then we get the absolute uncertainty of the volume, for that we need the volume:

V = π/4 * 5.1^2 * 37.6 = 768.1 cm^3

So:

ΔV = ±εV * V

ΔV = ±0.000228 * 768.1 = ±0.175 cm