SOLUTION: which would have a greater change in volume, an aluminum sphere with a radius of 0.4m at 2 degrees celcius that is raised to 45 degrees celcius, or a copper cylinder of radius 0.2m

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Question 203964: which would have a greater change in volume, an aluminum sphere with a radius of 0.4m at 2 degrees celcius that is raised to 45 degrees celcius, or a copper cylinder of radius 0.2m height 3m at 14 degrees celcius that is raised to 35 degrees celcius?
Answer by RAY100(1637) About Me  (Show Source):
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Volume of sphere = (4/3) pi *r^3
.
Delta V = (4/3) pi *{ (alpha) (*r)*(delta T) }^3
.
alpha for alum = 24 * 10^-6,
Radius = .4 m
delta T = (45-2)=43 deg C
.
Delta V = (4/3) pi * { (24*10-6) * .4 * 43)}^3 = 2.946 *10^-10
.
.
Volume of Cylinder = B*h = (pi * r^2) * h
.
Delta V = pi { (alpha)(r)(delta T)}^2 * { (alpha)(h)( delta T)}
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alpha copper = 17 *10^-6
r=.2
h=3
delta T = (35-14) = 21
.
delta V = pi *{(17*10^-6)(.2)(21)}^2 * {(17*10^-6)(3)(21)}
.
delta V = 1.7153 *10^-11
.
Therefore the alum sphere has greater volume change
.
approx 3*10^-10 vs 2*10^-11