See http://codex.wordpress.org/Function_Reference/get_term_by
The following code will work for your situation:
$cat = get_term_by( 'slug', 'aeroplane', 'category');
echo $cat->name;
See http://codex.wordpress.org/Function_Reference/get_term_by
The following code will work for your situation:
$cat = get_term_by( 'slug', 'aeroplane', 'category');
echo $cat->name;