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!)
volume of cup{V} = 1/3 x П x 12 x r²
ReplyDeleteV = 4Пr²
volume of water {V’/2} = 1/3 x П x h x r²
V’/2 = (hПr²)/3
V’ = (2hПr²)/3
compare {V} and {V’}
4Пr² = (2hПr²)/3
12Пr² = 2hПr²(the"Пr²"are cancel from both side)
12 = 2h
h = 6
or,one more method that can be use is just take a ruler and measure the water level...it'll be easier to see the level of water...OK...XD
chandy andrian {22}
3E1
10/3/2009
volume of cup{V} = 1/3 x П x 12 x r²
ReplyDeleteV = 4Пr²
volume of water {V’/2} = 1/3 x П x h x ((r²h²)/144)
V’ = (2h³Пr²)/432
compare {V} and {V’}
4Пr² = (2h³Пr²)/432
1728Пr² = 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
pour the water until the cone is full of water and then pour out the water until the cone is empty. hence we do not need to find the level of the water, rather than you think so hard that make you confuse...
ReplyDeleteno idea.. ~_~!
ReplyDeletebecause the two cones are similar and the ratio of volume is 1/2
ReplyDeletethe ratio of height is the cube root of 1/2 which is 0.794
therefore,h=12×0.794=9.52cm
This comment has been removed by the author.
ReplyDeleteyou just need a ruler to do this Q.
ReplyDeletehow to do is very simple:
~take your ruler and measure the height of water
this is the easiest way i can think of..
adela charissa the (1)
3e1
take a ruler or any measuring ruler, then measure it.. after measuring, you get the result, and that will be your final answer..
ReplyDeletedone..
Evelyn (5)
3E1
since the water level is half of the cone,
ReplyDeleteh=12/2
=6cm (super duper perfect answer)
=)
Vorapong,3E1
This comment has been removed by the author.
ReplyDelete1st step:
ReplyDeleteRead the question carefully…….
2nd step:
Since the height of the cone is 12cm and the water level [h] is half,
use your common sense….
3rd step:
Again, think carefully….
4th step:
Finally, you will get the answer
[h] is equal to 6cm
=)
Poom!!
3E1
This comment has been removed by the author.
ReplyDeleteCall the supplier, ask them what's the height of exactly half the volume of the cone.
ReplyDeleteLmao xD
The volume of the cup = 1/3∏ ×12×r²
ReplyDelete=4∏r²cm³
The volume of the water = 4∏r²× 1/2
=2∏r² cm³
1/3∏r²h = 2∏r²
h = 6
so the water level is 6 cm.
From Nguyen Thi Bich Hang(15) 3E1
First use a marker draw(line) the height of the water then Take a sisscor, cut the cone into half became a circle which lost a quarter of its paper... then use a ruler to measure the line of the marker which is being marked ... then i tink ans is 6 cox they say half mah cox full height is 12..
ReplyDeleteAsk zhen yi he's expert!!
ReplyDeletewhose zhen yi? =.=
ReplyDeleteNo need to think too much!!
ReplyDeleteJust take a ruler and measure the height of
the water!!..that's all~
i think this method not only is the easiest
one but also save time!! ^ ^
chen chia chi :)
Use the beaker with labels of volume.
ReplyDeletePour all the water inside into the beaker and measure the volume.
DONE~
by
JAMES BOND. 3e1
:)
ermm...
ReplyDeletejust use ruler and measure the h:)
but the easiest way is~~~
since the water in the paper cup will be drunk sooner or later,
why bother counting the h
waste time,paper and ink only!
then our brain will overwork! so might as well no need to do~!
JUWITA(6)
3E1
First fill the cone to the brim with water, then pour all that water into a beaker, pour back half the amount water from the beaker into the cone and measure from the vertex to the water level to get h- EKA
ReplyDeletethe ratio of volume of the two cones is 1/2
ReplyDelete,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 is
9.52cm(3sf)
PARK(32)
3E1 !! hahahaha
DIEGO JULIO FUJIANA (23)
ReplyDelete3E1
Method 1
What you need is a ruler and marker. Mark a dot on the paper cup, measure the h.
Method 2
Since height of cone is 12 cm, the height of cone when water filled half the cup is 12/2= 6 cm.
Since the two cones are similar,
ReplyDeletethe 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 is
9.52cm(3sf)
PARK(32)
3E1 !! hahahaha
hello!
ReplyDeletethe unknown water level = h cm.
the method is just to look at the picture. i think it's easy enough for us to determine that it is h cm. hehehe:D
Non-mathematical method
ReplyDeleteUse a ruler to measure the h !
Mathematical method
the volume of cone=4Пr²
the volume of water=1/3Пr²h
Therefore,2Пr²=1/3Пr²h
h=6cm
Rong Zi(18)
3E1
using the ruler is not the easiest!!!
ReplyDeleteu need to wait till the water stop moving, i mean need to wait untill it stop.....
cuz u will not get the exact value!!!!
lols!!
juz use common sense to ans lah!!!
PooM!!~
i think the simplest and easiest way to solve this Q:
ReplyDeleteJust take a ruler and measure the height of the water!
*!Lu Yue(13)
3E1
find the length of radius of cone, find the radius of the water(cone shape), then use the properties of similar cones to find h,
ReplyDeletehtet aung hlaing
3e1
This two inverted cones are similar.
ReplyDeleteLet 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√2
h = 12/ ³√2
h = 9.5244 ≒ 9.52
Ans. 9.52 cm.
3E1 Ou Yi Hsuan 17
The ratio of the volume is 1/2.
ReplyDeleteso, the ratio of the height is The cube root of 1/2.
The cube root of 1/2=h/12
h=9.25
Xiaoyan(10) 3E1 O(∩_∩)O
Find (water level h cm), such that (the volume of water is half the capacity of the cup).And height 12cm of paper cup cone
ReplyDeletetherefore the volume of cone =1/3(¶r2)(height)
1/3 x ¶r2(12)=4¶r2
Furthermore what is r?
let r be unknown
therefore the volume is half so
(4¶r2)/2=2¶r2
2¶r2/(1/3(¶r2))=height
AND THE ANSWER IS 6 ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
which mean u can just divide it by 2 and it done OMG
CAN I REQUEST THAT DONT GIVE ALL THIS QUESTION
CAUSE IT WASTE BOTH MY TIME AND MY EFFORT TO DO IT
DONE BY EXTRA (ZENG YI)3E1 (28)
DONE IT BECAUSE OF POPULAR REQUEST TO BE
EXTRA
THK U Q{^.^Q)
Just take the height of the cone and divide it by 2 because the height of the smaller cone is half the height of the bigger cone.
ReplyDeleteHannah(:
Please give us the correct answer
ReplyDeleteThank you for your kindness.