Thermal Expansion: Solving for Temperature Change

[izelkay]

Homework Statement

A hole in an aluminum plate has a diameter of 1.178 cm at 23 degrees Celsius. (a) What is the diameter of the hole at 199 degrees Celsius? (b) At what temperature is the diameter of the hole equal to 1.176 cm?

Homework Equations

The coefficient of linear expansion (α) for Aluminum is 24 x 10^-6

Formula to use, I think: ΔA = 2αAΔT
Where A = Area
T = Temperature
α = coefficient of linear expansion

The Attempt at a Solution

I'm having trouble solving part (b).

I keep getting the ΔT to be -502 degrees, which seems like way too much.
What I did first was convert everything from centimeters to meters, and solved for the original area

A = pi(0.0089)²
= 2.49 x 10^-4

And solved for the new Area, A'

A' = pi(0.0088)²
= 2.43 x 10^-4

Subtracted A from A' to get ΔA
A' - A = -6 x 10^-6

Solved for ΔT in formula

ΔA = 2αAΔT

ΔT = ΔA / 2αA

= -6 x 10^-6 / [2(24 x 10^-6)2.49 x 10^-4]
= -502

Again, that seems like too much of a temperature change...can anyone help?

 

[izelkay]

Anyone...?

 

[izelkay]

Never mind, I got it.