Question

For my lab report, i was asked to find the volume uncertainty of different cylinders:

	Length m	Diameter m (r = d/2)
A	0.0407 ± 0.00025 m	0.0179 ± 0.0005 m
B	0.0377 ± 0.00025 m	0.0317 ± 0.0005 m
C	0.0361 ± 0.00025 m	0.019 ± 0.0005 m
D	0.0462 ± 0.00025 m	0.0158 ± 0.0005 m
E	0.0339 ± 0.00025 m	0.019 ± 0.0005 m

in the table below, its the volume but what I NEED IS ITS UNCERTAINTY:

V = (PI)(r)(h)

Cylinders	Volume convert to m^3 and find the uncertainty
A	1.024 * 10^-5
B	2.975 * 10^-5
C	1.023 * 10^-5
D	9.05 * 10^-6
E	9.61 * 10^-6

Answer 1

first go through the image to understand the concept

in case 3

cylinder C

Percentage uncertainty in the length = (0.00025/0.0361) x 100 = 0.070
Percentage uncertainty in the diameter= (0.0005/0.019) x 100 = 2.631
% uncertainty = 0.070 + 2.631 = 2.701
volume = 1.023 *10^-5
Absolute uncertainty in volume = (1.023*10^-5/100) x2.701 = 0.0000002763

case 4

cylinder D

Percentage uncertainty in the length = (0.00025/0.0462) x 100 = 0.541
Percentage uncertainty in the diameter= (0.0005/0.0158) x 100 = 3.164
% uncertainty = 0.541 + 3.164 = 3.705
volume = 9.05 *10^-6
Absolute uncertainty in volume = (9.05*10^-6/100) x3.705 = 0.0000003353

case 5

cylinder D

Percentage uncertainty in the length = (0.00025/0.0339) x 100 = 0.737
Percentage uncertainty in the diameter= (0.0005/0.019) x 100 = 2.631
% uncertainty = 0.737 + 2.631 = 3.368
volume = 1.023 *10^-5
Absolute uncertainty in volume = (9.61*10^-6/100) x3.368 = 0.0000003237