SOLUTION: You are making an arrangement with 13 cylindrical beeswax candles where all the candles are three times as tall as they are wide. If you want the 3 medium candles to be twice the h

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Question 972664: You are making an arrangement with 13 cylindrical beeswax candles where all the candles are three times as tall as they are wide. If you want the 3 medium candles to be twice the height of the 9 small candles and the large candle to be three times as tall as the small candles, find the maximum height and diameter of the candles you can make from a 10 pound block of beeswax, given that one pound of beeswax has a volume of approximately 28.622 cubic inches. Round your answers to the nearest hundredth of an inch.
I know that the volume of cylinder is= pir^2h (small candles)
So are the medium candles pir^2(2h)
and the large candle pir^2(3h)
but it also says 3times as tall as they are wide so do I multiply that at the end?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You are making an arrangement with 13 cylindrical beeswax candles where all the candles are three times as tall as they are wide.
If you want the 3 medium candles to be twice the height of the 9 small candles and the large candle to be three times as tall as the small candles, find the maximum height and diameter of the candles you can make from a 10 pound block of beeswax,
given that one pound of beeswax has a volume of approximately 28.622 cubic inches. Round your answers to the nearest hundredth of an inch.
:
let x = the radius of the smaller candle (the width or diameter is 2x)
then
6x = height of the smaller candle (3 times the diameter which is 2x)
:
Medium candle height would be be = 12x (twice the height of the smaller
then
2x = the radius of the medium candle (1/6 of the height of the medium)
:
Large candle height would be = 18x (3 times the height of the smaller)
then
3x = the radius of large candle (1/6 time the the height of the larger)
:
Volume equation
9(pi*x^2*3x) + 3(pi*(2x)^2*12x) + (pi*(3x)^2*18x) = 10*28.622
9(9.4258x^3) + 3(150.7964x^3) + 508.938x^3 = 286.22
do the math
1046.1594x^3 = 286.22
x^3 = 286.22%2F1046.1594
x^3 = .2736
Find the cube root
.649 inch is the radius of the smaller candle
then
1.298 inches diameter and 3.895 inches the height of the smaller candle
:
The medium candle
4(.649) = 2.596" is the diameter and 7.788" is the height of the medium
:
the large candle
6(.649) - 3.984" is the diameter and 11.682" is the height of the large