physics help..i'll really appreciate it...this is my review for finals.?

Question

1.A concrete highway is built of slabs 14m long (20 degrees celcius). How wide should the expansion cracks be at 20 degrees celcius) between the slabs to prevent buckling if the range of temperature is -30 degrees celcius to +50 degrees celcius?
2.A quartz sphere is 14.5cm in diameter. What will be its change in volume if it is heated from 30 degrees celcius to 200 degrees celcius?

Answer 1

1.
Gap min = L(20) -L(50)

Gap min = kL(T2-T1)
Gap min = 14E-6 x 14 (50 - 20)=0.00588 m
Gap min=0.588 cm

2.
V=(4/3) pi R^3
Change in dV=V2-V1
V1=(4/3) pi R^3
V2=(4/3) pi (R+dR)^3
dR= k R(T2-T1)

dV= (4/3) pi ( (R+dR)^3 -R^3)
dV= (4/3) pi ( (R+k R(T2-T1))^3 - R^3)
dV= (4/3) pi R^3( (1+k(T2-T1))^3 - 1)

T2=200 C T1=30C
Just plug the numbers.