MAXIMUM VOLUME OF A CONE
Task Goal
- To find the maximum volume of a paper cone formed by a fixed radius
- To find the maximum volume of a paper box formed by a square (20 cm long)
Focus
- Calculate the volume of a cone and an open box
- Compare results
- Summarize with tables or graphs with / without spreadsheet
TASK 1
Given a circular paper, we can fold it into a cone
![[size=100][size=150][size=85]Obtained from http://www.had2know.com/academics/maximum-volume-cone-from-circle.html[/size]
[/size][/size]](https://www.geogebra.org/resource/DzcyNqw5/jinOZcrc5aiHFzOV/material-DzcyNqw5.png)
![[size=100][size=150][size=85]Obtained from http://www.had2know.com/academics/maximum-volume-cone-from-circle.html[/size]
[/size][/size]](https://www.geogebra.org/resource/ArBqZD5N/s2Pt0GmOsSrlMgcQ/material-ArBqZD5N.png)
![[size=100][size=150][size=85]Obtained from http://www.had2know.com/academics/maximum-volume-cone-from-circle.html[/size]
[/size][/size]](https://www.geogebra.org/resource/zFzBM3uQ/v1OxDFb87thWSrZh/material-zFzBM3uQ.png)
Task 1.1
Move the point on the circle and observe the change of the volume of the cone
To MAXIMIZE the volume of the cone, how large should the angle be?
This is the END of Task 1
![[size=100][size=150]
[/size][/size]](https://www.geogebra.org/resource/VR2GePdq/LQ4BO5IeEL2fizT8/material-VR2GePdq.png)
TASK 2
Given a square paper, we may also fold it into a box
![[size=85]Obtained from http://thinkcrafts.com/blog/2012/08/21/a-note-for-the-teacher-box/[/size]](https://www.geogebra.org/resource/A79MDeUm/66arCNzQanuNQ7hV/material-A79MDeUm.png)
![[size=85]Obtained from http://thinkcrafts.com/blog/2012/08/21/a-note-for-the-teacher-box/[/size]](https://www.geogebra.org/resource/qJAT4ntC/UG3lfFUEQ7RGU54K/material-qJAT4ntC.png)
Task 2.1
Move the blue point to change the size of box folded
To MAXIMIZE the volume of the box, how long should AB be?
This is the END of Task 2 and this Worksheet
