# Uncertainity and Error Question

1. Feb 23, 2008

### inno87

I'm not sure if I am doing this right, can anyone help me out?

A cylindrical cookie has a diameter of 5.0 $$\pm$$ 0.1 cm, and a thickness of 1.00 $$\pm$$ 0.01 cm.

A. Assuming the uncertainities are normally distrubited, what is the most likely value of the volume of the cookie?

V=pi*(d/2)^2*h=pi*(1 $$\pm$$ .01 cm * [(5.0 $$\pm$$ .1 cm)/2]^2=pi*[1 $$\pm$$ .01 cm * (2.5 $$\pm$$ .05 cm)^2=pi*[1 $$\pm$$ .01 cm * 6.25 $$\pm$$ .1 cm^2]=pi* 6.25 $$\pm$$ .11 cm^3 = 19.634 $$\pm$$ .11 cm^3

Most likely volume is 19.634 cm^3

B. What is the percent uncertainty in the volume?
.11/19.634=.5603%

C. What is the absolute uncertainty in the volume?
.11 cm^3 (taken from question 1)

D. Assuming the thickness uncertainity remains $$\pm$$ .01 cm, to what value would the diameter's uncertainty (in cm) have to be reduced in order to make the uncertainty in the volume $$\pm$$ 3%?

I tried setting up something like (.01+D_unc)/(19.634)=.03 but that would mean you'd have to increase the uncertainty so it seems I may have done something wrong here!

2. Feb 25, 2008