p19_022.pdf

22. (a) Since A = πD 2 / 4, we have the diﬀerential dA =2( πD/ 4) dD . Dividing the latter relation by the

former, we obtain dA/A =2 dD/D . In terms of ∆’s, this reads

∆ A

=2 ∆ D

for

∆ D

1 .

We can think of the factor of 2 as being due to the fact that area is a two-dimensional quantity.

Therefore, the area increases by 2(0 . 18%) = 0 . 36%.

(b) Assuming that all dimension are allowed to freely expand, then the thickness increases by 0 . 18% .

(d) The mass does not change.

(e) The coe1cient of linear expansion is

α =

∆ D

D ∆ T =

10 − 2

100 ◦ C

=18

10 − 6 / C ◦ .

0 . 18