Thermal expansion (Simple) (attempt posted)

[Bjorn J]

Homework Statement

I'm looking for a good explanation, not interested in the answer.

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 on a winter day at a temperature of -18 C.

How much more interior space does the dome have in the summer when the temperature is 30 C?

Relevant equations:
1. For length: Delta L = alpha (L initial) ( Delta T)
2. For Volume: Dela V = Beta (V initial) ( Delta T)

Attempt:

I attempted to calculate the surface area of the hemisphere by dividing the surface area of a sphere by 2.
= 6361m
Coming to calculate the area of increase, this is where I got stuck. I was not given any coefficients, and from my knowledge they are obtained experimentally.

I'm guessing I'm approaching this problem incorrectly.

Thanking you in advance for a detailed explanation of how to obtain how much the dome increased.

Bjorn.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

I attempted to calculate the surface area

Why are you calculating surface area? The question asks about interior space.