- #1

SiriusAboutAstronomy

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## Homework Statement

A ring of aluminum has a hole in the middle. When the ring is heated:

a) the hole decreases in diameter

b) the aluminum expands outward and the hole remains the same size.

c) the area of the hole expands by the same percent as the area of the aluminum.

d) the area of the hole expands by a greater percent than the area of the aluminum.

e) the linear expansion causes the hole to expand in a slightly elliptical pattern.

## Homework Equations

ΔA=[itex]\alpha[/itex]AΔT

[itex]\alpha[/itex]=area thermal expansion coefficient

A=area

T=temperature

## The Attempt at a Solution

I know the hole gets larger. What I can't figure out is whether the hole expands by the same percent of the area of by a greater percent. I want to say that it will expand at a greater percent because the metal expands everywhere in one dimension but area is in two dimensions (if that makes any sense).

Like the area of the circle is ∏r

^{2}, but the area of the ring is ∏(R

^{2}-r

^{2}) with big R being the outer radius and little r being the inner radius. Because of this formula, wouldn't the inside expand by a greater amount than the outside.

I've been thinking about this problem so long I've kinda gotten burnt out at looking at it from any other angles...