45 points for first most detailed / accurate you are planning to make and sell 3 different sizes of cylindrical candles. you buy 1 cubic foot of candle wax for $20 to make 24 candles (8 per 3 sizes). a. design the candles what dimensions are each size of candle? (remember, 3sizes) b. you want to make a profit of $100. decide on a price for each size of candle. c. did you set the prices so that they are proportional to the volume of each size of candle? why/why not?

A.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions. 

I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.

With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:

V=pi(r^2)(h)

we then solve the corresponding height per candle. Let us let the value of pi be 3.14.

Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for 

r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in

b. each candle should sell for $15.00 each

($20+$100)/8=$15.00

c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes