Tuesday, March 31, 2009

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!

Monday, March 9, 2009

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!)

Friday, March 6, 2009

Introduction

Welcome to Bedok Town's First Math Blog!

Look out for Math riddles, Math trivia and other Math info and other cool stuff!
Feel free to leave comments if you have any!

P. S. Do suggest new ideas! ;-)