A wooden box measures $$\(30 \mathrm{~cm}\)$$ by $$\(15 \mathrm{~cm}\)$$ by $$\(32 \mathrm{~cm}\)$$. The box has a lid. A carton measures $$\(5 \mathrm{~cm}\)$$ by $$\(5 \mathrm{~cm}\)$$ by $$\(5 \mathrm{~cm}\)$$. James has 110 cartons. He wants to put all these cartons in the box and be able to shut the lid. Can James put all 110 cartons in the box and shut the lid? Show your working clearly.

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