- #1
inno87
- 6
- 0
I'm not sure if I am doing this right, can anyone help me out?
A cylindrical cookie has a diameter of 5.0 [tex]\pm[/tex] 0.1 cm, and a thickness of 1.00 [tex]\pm[/tex] 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 [tex]\pm[/tex] .01 cm * [(5.0 [tex]\pm[/tex] .1 cm)/2]^2=pi*[1 [tex]\pm[/tex] .01 cm * (2.5 [tex]\pm[/tex] .05 cm)^2=pi*[1 [tex]\pm[/tex] .01 cm * 6.25 [tex]\pm[/tex] .1 cm^2]=pi* 6.25 [tex]\pm[/tex] .11 cm^3 = 19.634 [tex]\pm[/tex] .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 [tex]\pm[/tex] .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 [tex]\pm[/tex] 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!
A cylindrical cookie has a diameter of 5.0 [tex]\pm[/tex] 0.1 cm, and a thickness of 1.00 [tex]\pm[/tex] 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 [tex]\pm[/tex] .01 cm * [(5.0 [tex]\pm[/tex] .1 cm)/2]^2=pi*[1 [tex]\pm[/tex] .01 cm * (2.5 [tex]\pm[/tex] .05 cm)^2=pi*[1 [tex]\pm[/tex] .01 cm * 6.25 [tex]\pm[/tex] .1 cm^2]=pi* 6.25 [tex]\pm[/tex] .11 cm^3 = 19.634 [tex]\pm[/tex] .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 [tex]\pm[/tex] .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 [tex]\pm[/tex] 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!