How to query (xmla) the size of an OLAP catalog in MSAS2008?

Question

I would like to be able to query against an SSAS2008 instance and get a listing of all the catalogs that exist in it, as well as their respective storage sizes. In Management Studio, I can right click on the catalog and go to its properties, which retrieves this data, so I know it exists somewhere. A query that has some of the information I need is below:

<Discover xmlns="urn:schemas-microsoft-com:xml-analysis">
  <RequestType>DBSCHEMA_CATALOGS</RequestType>
  <Restrictions />
  <Properties />
</Discover>

Answer 1

<Discover xmlns="urn:schemas-microsoft-com:xml-analysis">
  <RequestType>DISCOVER_XML_METADATA</RequestType>
  <Restrictions />
  <Properties />
</Discover>

Cube Name = <return><root><row><xars><Server><Databases><Database><Name>
Estimated Size = <return><root><row><xars><Server><Databases><Database><EstimatedSize>