Grades 9-10 Video Solutions 2026-2026_9-10

Video Transcription

Video Summary

The solution uses the two bottle positions to compare the water-filled cylindrical part and the empty cylindrical part. Let the bottle’s radius be \(R\).  <br /><br />- In the first position, water forms a cylinder of height \(24\), so its volume is \(24\pi R^2\).<br />- In the flipped position, the empty part forms a cylinder of height \(42 - 30 = 12\), so its volume is \(12\pi R^2\).<br /><br />Thus, the empty volume is half the water volume. Since total capacity is \(4.5\) liters, we have:<br /><br />\[<br />\text{water} + \text{empty} = \text{water} + \frac{1}{2}\text{water} = \frac{3}{2}\text{water} = 4.5<br />\]<br /><br />So the water volume is \(3\) liters.

Keywords

water volume

cylindrical bottle

bottle positions

volume ratio

liters