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?

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)   (Show Source): You can put this solution on YOUR website!
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(52855)   (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 = Cancel in both sides and substitute the given data = *16 = 9 = = = R = = . ANSWER. The diameter of the produced candles is = 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)   (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, = 9. So, 9 = Therefore, radius of each small candle, or As such, diameter of each small candle = 2R = 2(.5) = 1 cm.

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