Things to consider for Math Riddle 1...

What volume of water does a similar cone of height 6cm contain compared to a cone of height 12cm?
(Note that the volume is not halved, because the radius for the 6cm cone has also been halved)

Results of Math Riddle 1

Here are the best 3 unique answers:

(1) volume of cup{V} = 1/3 x П x 12 x r²
V = 4Пr²
volume of water {V’/2} = 1/3 x П x h x ((r²h²)/144)
V’ = (2h³Пr²)/432
compare {V} and {V’}
4Пr² = (2h³Пr²)/4321728Пr² = 2h³Пr²(the "Пr²" are cancel from both side)
1728 = 2h³
h³ = 864
h = ³√864
h = 9.524403612
h ≈ 9.52 (3sf)

Yose {30}3E1 11/3/2009


(2) This two inverted cones are similar.
Let a: b to be the ratio of this two similar cones.
a³: b³ = 1 : 2 a : b = ³√1:³√2= 1 : ³√2
The ratio of height is a : b
Thus h : 12 = 1 : ³√2h = 12/ ³√2h = 9.5244 ≒ 9.52
Ans. 9.52 cm.3E1

Ou Yi Hsuan 17


(3) Since the two cones are similar,
the ratio of volume of the two cones is 1/2,
so the ratio of the height of the two cones is cube root of 1/2 which is 0.794(3sf).
Therefore, h = 12 x cube root of 1/2
which is9.52cm(3sf)

PARK(32)


Congratulations to Yose, Yi Hsuan and Park.
Do collect your prizes from your Math teacher.
A big thank you to all those who provided solutions and comments.
Better luck next time!

Math Riddle 1: Cone paper cups

There are some paper cups at a drinking fountain. Each cup is in the form of an inverted cone of height 12cm.

Determine a method, mathematical or non-mathematical, to find the water level h cm, such that the volume of water is half the capacity of the cup.

(Give your answers in the comments section below - Prizes will be awarded for best 3 unique answers!)

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