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?

ΔV = ±0.175 cm

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

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)