1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Thermal Expansion of a hemisphere

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    Linear Expansion: delta L=alpha(L_original)(delta T)
    Volume Expansion: delta V=(3)alpha(V_original)(delta T)

    3. The attempt at a solution

    Ok so I for this question I treated it as a sphere and halved my answer because I though it made sense, not sure if it really mattered

    First attempt:
    I calculated the original volume of the sphere, which is 47713 m^3. And then I used the volume expansion to calculate the increase in the volume of the sphere which was
    delta V=3(2.4*10^-5)(48)(47713) = 164.9L and divide this by 2 and you get 82.4L
    But this is wrong

    Second attempt:
    I tried linear expansion, this way makes near to no sense so I'll abreviate it, I used the linear expansion formula to calculate directly the increase in the radius, and then from there calculated the increase in volume, didnt work

    Third attempt: I thought I had it this time
    Firsty I calculated the surface area of the sphere = 6361.73
    Then calculated the area increase which is delta A=(48)(6361.73)(2)(2.4*10^-5) = 14.66m^2878.53
    The calculated the new area =6376.39
    Then the new radius, sqrt(6376.39/4Pi) = 22.526 So the new volume of the sphere= 47878.53. Original volume= 47712.93.....47878.53-47712.93 =165.6 for a sphere
    Volume increase for hemispere= 82.8 m^3 Is this right? Because I'm using masteringphysics and I said 82.5 by mistake and it didnt say I was even close to the answer, I only have one attempt to get this right so I dont want to get it wrong.

    Thanks very much for the help, sorry if its a bit convoluted, my first time posting.
  2. jcsd
  3. Jan 20, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Samonasuke! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    No, the volume will be 2/3 πr3 = 1/12 πd3
  4. Jan 20, 2010 #3
    I was working with a full sphere and then divided my answer in half at the end, anyway I found out where I was going wrong!!!!! I cant believe it, I thuoght tha 55/2 22.5 :O Terribly stupid mistake!!!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Thermal Expansion hemisphere Date
Thermal expansion of a ring Feb 27, 2018
Thermal expansion of bimetallic strip Dec 24, 2017
Thermal expansion May 18, 2017
Find the change in height of a bridge Apr 29, 2017
Thermal expansion (Simple) (attempt posted) May 20, 2015