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CH-21-001 · Cone transfer, cylinder capacity and overflow

17 cm6 cmr = 7 cm9 cm
Diagram not accurately drawn

A full conical vessel has radius 6 cm and vertical height 17 cm. Its contents are poured into an initially empty cylinder of radius 7 cm and height 9 cm. This is repeated 7 times, using a full cone each time. Find the final water depth in the cylinder and the volume of water that overflows, in litres. Give both answers to 2 decimal places.

3D Shapes: Cone-to-Cylinder Volume Transfer Booklet p. 39 & p. 40
Method
1) Total poured volume = n × (⅓πr²h)
2) Cylinder capacity = πR²H
3) Compare to find depth and divide overflow cm³ by 1000 for litres
Worked Example (CH-21-001)
1)
Cone volume = 13π(6)2(17)\frac13\pi(6)^2(17).
2)
Multiply by 7 for total water volume.
3)
Cylinder capacity = π(7)2(9)\pi(7)^2(9).
4)
Compare supplied volume with capacity; final depth is the smaller of container height and volume ÷ base area.
5)
Depth 9.00 cm.
6)
Overflow = max(0, supplied volume − capacity); divide cm³ by 1000.
7)
3.10 litres.
Ans = Depth 9.00 cm; overflow 3.10 litres.