i am guessing the circle is a hollow sphere...
... as opposed to, say, a solid sphere... or a solid disk... what are you basing your guess on?
note: a hollow sphere is commonly represented by a circle while a solid one would be represented by a colored-in circle... but maybe the person setting the question does things differently?
... and the rectangle a solid cylinder...
... why a hollow for the first shape and solid for the second one? Why not the other way around or maybe both hollow or both solid?
It's OK to make
educated and
informed guesses - but it is never OK to make blind guesses.
...and that the thing rotates about the axis out of the page
... OK. The working you did is for rotating about an axis along the length of the "cylinder". For an axis out of the page, where is the axis of rotation on the figure? The correct moment of inertia depends on it's position. Or, maybe, the question is just asking for which com inertias to apply the parallel axis theorem to? In which case, you want to look more closely at which com moment you have used for the "cylinder".
What I'm getting from your reply is that you do not know which axis is intended or what objects the shapes on the drawing are intended to represent. This is forcing you to make a LOT of assumptions. Bottom line is that you don't have enough information to complete the question as written.
If the question is really so wide open, you will need to make some sort of argument to support your assumptions. Maybe other questions like this one have used hollow spheres and solid cylinders? But maybe what is written above is not the complete problem statement as it was given to you? Right now it is not possible to properly advise you.
