What I had to  do to solve this candle box problem  was know the formula on how to solve for the surface area of the prism. My first step was getting one of the hexagonal and draw it separate from the rest with the information given. The information given was that the diameter was 6 cm and the height was 10 cm. You would have to section out the hexagon to 6 triangles and draw one right triangle to the side with the hypotenuse  being 3 cm because the hypotenuse is like the radius. So then you have a special right triangle of 30, 60 ,90 so to find the short leg you have to divide the hypotenuse by 2 so you would have the short leg as 2\3. To find the long leg you have to multiply the short leg by the √3 and you get 3√3 \2. The formula to find the area of the hexagon is            A=(a)(p)\2 so you would do (3√3)(18)\2 and the answer would be 27√3 but you would have to multiply that by 2 because there are 2 bases. So the final answer for the hexagon is A=27√3. However there is also 6 rectangles and to find the area of the that you have to do A=bh and the height of the rectangle is 10 and the base is 3. So it would be 3x10 and that would equal 30 but then you have to multiply that by 6 because there are 6 rectangles and you would get A=180. So the final answer for the surface area of the prism = (27√3 +180)cm^2. But since the thin paper costs $.01 you would multiply that by the answer and the total is 2.27.


Then i had to find the surface area of the cylinder. to do that i had to use the formula to find the area of a circle and the area of a rectangle too. To find the area of a circle which in this  case is the base the radius would be 3 so in the formula πr^2  you'd substitute it in to π(3)^2  so π9 and you would multiply it by 2  because they are bases and you would get 18π. Then you would add the area of the rectangle A=bh and that would be A=(6π) (10) and you would get 60πcm^2 and your total answer is 78πcm^2. But then you have to multiply that by $.02 because  that is what the second box costs. You're total answer will be 3.7.

To find out how much Blace has to sell his candels for in order for him to get 20% profit he you have to multiply 15x.2 then add the 15 back and add 2.3 and 3.7 and the final answer will be $24!