$\pi h$ and $ 3^2\pi h$
Am I supposed to insert 20 cm and 28 cm somewhere in the expression?
I have no idea how to start off this question.
2026-03-31 12:16:30.1774959390
Height of a bottle, given internal water levels in two orientations
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Let $x$ be the height of the column of air when the bottle is right-side-up. Since the volume of this empty space remains unchanged when the bottle is turned over, we have $$\pi\cdot1^2\cdot x=\pi\cdot3^2\cdot(x-8)$$ where the 8 comes from the given difference in water level between the two orientations. Solving for $x$: $$x=9(x-8)=9x-72$$ $$8x=72$$ $$x=9$$ The height of the bottle is therefore $20+x=20+9=29$ centimetres.