SOLUTION: You are designing candle-making kits. Each kits contain 25 cubic inches of candle wax and a mold for making a pyramid-shaped candle wiht a square base.You want the height of the ca

Algebra ->  Volume -> SOLUTION: You are designing candle-making kits. Each kits contain 25 cubic inches of candle wax and a mold for making a pyramid-shaped candle wiht a square base.You want the height of the ca      Log On


   

Question 1089033: You are designing candle-making kits. Each kits contain 25 cubic inches of candle wax and a mold for making a pyramid-shaped candle wiht a square base.You want the height of the candle to be 2 inches less than the edge of the base. What should the dimension of the candle mold be? show a mathematical procedure in determining the dimension
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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You are designing candle-making kits. Each kits contain 25 cubic inches of candle wax and a mold for making a pyramid-shaped candle wiht a square base.
You want the height of the candle to be 2 inches less than the edge of the base.
What should the dimension of the candle mold be? show a mathematical procedure in determining the dimension
:
let s = the side of the base
then
(s-2) = the height of the pyramid
:
Vol of pyramid = 1%2F3 * base area * height
V = 25, therefore
1%2F3*s^2*(s-2) = 25
multiply both sides by 3, get rid of the fraction
s^2*(s-2) = 75
s^3 - 2s^2 = 75
s^3 - 2s^2 - 75 = 0
Graph this equation
+graph%28+300%2C+200%2C+-6%2C+10%2C+-100%2C+200%2C+x%5E3-2x%5E2-75%29+
solution is s = 5
:
See if that checks out
1%2F3*5%5E2%2A3 = 25