Question

Constants As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 7 0x102+ 0.005 cm

Find the average volume of a cookie.

Find the uncertainty in the volume of a cookie.

The ratio of the diameter to the thickness is 120.

Find the uncertainty in this ratio.

Answer 1

d = 8.50 plusminus 0.02 cm t (thickness) = 7.0 times 10^- 2 plusminus 0.005 cm (a) Avg volume = pi (d/2)^2 t = pi times (8.50/2)^2 times 7.0 times 10^- 2 cm^3 v = 3.972 cm^3 (b) uncertainty in volume: plusminus delta v/v = 2 delta d/d + delta t/t plusminus delta v/dv = 2 times 0.02/8.50 + 0.005/7.0 times 10^- 2 implies delta v = plusminus v (2 times 0.02/8.50 + 0.005/7 times 10^- 2) = plusminus 0.0187 cm^3 (ans) (c) d/t = 120 implies delta d/dt = 120 d = 120 t volume = pi(d/2)^2 t = pi(120 t/2)^2 t = pi(60 t)^2 t v = pi 60^2 t^3 = 3600 pi t^3 implies delta v/v = 3 delta t/t implies delta v = 3 times v times delta t/t = 3 times pi t^3 times 3600 times delta t/t = (3 times 3600) pi t^2 delta t = 10800 pi t^2 delta t