SOLUTION: A wax candle is 16cm long and 1½cm in diameter, it is melted and made into 4 identical candles each of which is 9cm long. What is the diameter of these candles?

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Question 1205009: A wax candle is 16cm long and 1½cm in diameter, it is melted and made into 4 identical candles each of which is 9cm long. What is the diameter of these candles?
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
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the candle is 16 cm long and 1.5 cm in diameter.

it's volume is equal to pi * r^2 * h.
r is the radius.
h is the height.

radius is equal to half the diameter = 1.5/2 = .75 cm

volume is pi * .75^2 * 16 = 9 * pi

it is melted and made into 4 identical candles, each of which is 9 cm long.

you have a total volume of 9 * pi.
you divide that by 4 to get 4 identical volumes of 9/4 * pi.
each of them is 9 cm high.
the volume of each becomes pi * r^2 * 9 = 9/4 * pi
solve for r^2 to get r^2 = 9/4 * pi / pi / 9
simplify to get r^2 = 1/4 square cm.
solve for r to get r = sqrt(1/4) = 1/2 cm.
the diameter is twice that, so the diameter of each of the 4 candles is 1 cm.

if this is correct, then the volume of all 4 of the candles should be equal to the volume of the original candle.
that volume was 9 * pi.

the total volume of the 4 candles is equal to 4 * pi * .5^2 * 9.
this becomes equal to 9 * pi.
since it's the same volume as the original candle, it is correct and is your solution.

your solution is, as best i can determine, that the diameter of the 4 individual candles is equal to 1 cm each.



Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
.
A wax candle is 16cm long and 1½cm in diameter, it is melted and made into 4 identical candles
each of which is 9cm long. What is the diameter of these candles?
~~~~~~~~~~~~~~~~~~~~~~


        The shorter the solution, the clearer its meaning is. 


Equate the volumes

    pi%2Ar%5E2%2Ah = 4%2Api%2AR%5E2%2AH


Cancel  pi  in both sides and substitute the given data

    %281.5%2F2%29%5E2%2A16 = 4%2AR%5E2%2A9

    2.25%2F4*16 = 4%2AR%5E2%2A9

    9 = 36R%5E2

    R%5E2 = 9%2F36 = 1%2F4

    R = sqrt%281%2F4%29 = 1%2F2.


ANSWER.  The diameter of the produced candles is 2%2A%281%2F2%29 = 1 cm each.

Solved.

-------------------

Thanks to tutor @MathTherapy for noticing my error.

After his notice, I fixed my post, and now you see the updated / (correct) version.




Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
A wax candle is 16cm long and 1½cm in diameter, it is melted and made into 4 identical candles each of which is 9cm long. What is the diameter of these candles?

I totally agree with Tutor @IKLEYN that the shortest solution is best. I also agree that the shortest and easiest
method to get to the answer is to EQUATE the 2 VOLUMES. However, %281.5%2F2%29%5E2%2A16 = 9. So, 9 = 36R%5E2
                                                                                    matrix%282%2C3%2C+9%2F36%2C+%22=%22%2C+R%5E2%2C+1%2F4%2C+%22=%22%2C+R%5E2%29
                                     Therefore, radius of each small candle, or  
                                     As such, diameter of each small candle = 2R = 2(.5) = 1 cm.