Re: "Time Machine - how much space?" : "MacBook Air with an 8GB hard drive":
32GB hard drive / not enough space
Seems there must be some mistake ie: new MacBook Air models come with 256GB, 512GB, 1TB, or 2TB storage space, so a 32GB storage device would not be enough to back-up any recent models.
You might want to check which MacBook Air model you have:
How to: Identify your MacBook Air model - Apple Support
Eg: The Tech Specs for MacBook Air 2017 model say the smallest storage available at purchase was 128GB
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You can check how much storage is in use, and how much is free space, on your MacBook Air:
If you have macOS Ventura or later installed:
Choose Apple menu > System Settings, click General in the sidebar, then click Storage on the right.
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For earlier versions of macOS: Choose Apple menu > About This Mac, then click Storage.
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Apple Support's article:
How to: Back up your Mac with Time Machine - Apple Support
says:
"Ideally, your backup disk should have at least twice the storage capacity of every disk or volume you're backing up. If your backup disk doesn't have enough storage space to contain a complete backup, Time Machine will let you know."
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Re: I have a lot backed up on my cloud, so why is it taking so much space?
Seems iCloud is mainly used for sync. of data across various Apple devices.
Generally the data may be both on Mac and in iCloud:
See: What's the difference between device storage and iCloud storage? - Apple Support
and
How to: Archive or make copies of the information you store in iCloud - Apple Support
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Making use of that 32 GB drive:
If the drive is formatted for Mac:
You can back up files like documents, pictures, and movies by just dragging them to an external USB drive.
To restore them, just drag them back.