How to know the size of an object in memory ? c#

Question

Just to put it in context, I’m upgrading an image search engine and need to save the previous search to the session:

public static void SavePreviousSearch(APIStandardSearchResponse search)
{
    HttpContext.Current.Session[PREVIOUS_SEARCH_KEY] = search;
}

And I call it within a search process in which I mount a APIStandardSearchResponse:

SearchCookieController.SavePreviousSearch(APIStandardSearchResponse);

Then when necessary I retrieve this object:

APIStandardSearchResponse previousSearch = SearchCookieController.GetPreviousSearch();

I would like to know the memory space (on the server) that the object previousSearch is occupied. It is possible to do this with the c#?