SOLUTION: A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inche
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Question 1143127: A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles
You can put this solution on YOUR website! A candle manufacturer sells cylindrical candles in sets of three.
Each candle in the set is a different size.
The smallest candle has a radius of 0.5 inches and a height of 3 inches.
The other two candles are scaled versions of the smallest, with scale factors of 2 and 3.
:
Find the volume of the 1st candle
V1 =
V1 = 2.356 cu/in
Find the vol of the 2nd; r=1; h=6
V2 =
V2 = 18.850 cu/in
Find the vol of the 3rd; r=1.5; h=9
V3 =
V3 = 63.617 cu/in
:
" How much wax is needed to create one set of candles"
2.356 + 18.850 + 63.617 = 84.823 cu/inches
The amount of wax required depends on the volume of the set of candles.
(1) Determine the volume V of the smallest candle.
(2) With scale factors of 2 and 3, the ratios of the VOLUMES of the other two candles to the volume of the smallest are 2^3=8 and 3^3=27. So the total volume of the three candles is V + 8V + 27V = 36V.
