SOLUTION: You are designing a cone-shaped candle with a volume of 8 cubic inches. The height of a cone is 2 inches longer than the diameter of a base. What should be the diameter and hieght

Algebra ->  Volume -> SOLUTION: You are designing a cone-shaped candle with a volume of 8 cubic inches. The height of a cone is 2 inches longer than the diameter of a base. What should be the diameter and hieght       Log On


   

Question 814889: You are designing a cone-shaped candle with a volume of 8 cubic inches. The height of a cone is 2 inches longer than the diameter of a base. What should be the diameter and hieght of the cone
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = diameter of the base.
h=d+2 where h is height.
Volume, v=h%281%2F3%29pi%2Ar%5E3 and here, r=%281%2F2%29d so you could use volume formula as v=%28d%2B2%29%281%2F3%29pi%2A%281%2F2%29%5E3%2Ad%5E3
v=%28d%2B2%29%281%2F24%29pi%2Ad%5E3
.
and you would want to solve for d, because you were already given v=8 cubic inches.

v=d%28pi%2F24%29d%5E3%2B2%28pi%2F24%29d%5E3
v=%28pi%2F24%29d%5E4%2B2%28pi%2F24%29d%5E3
highlight%28%28pi%2F24%29d%5E4%2B%28pi%2F12%29d%5E3-8=0%29, using the given v=8.

At this extent, one would prefer to use a graphing calculator or some other software program to handle that cubic equation. The value of d which satisfies the equation would be (for positive d) the diameter...

Trying the function in Google as y=%28pi%2F24%29x%5E4%2B%28pi%2F12%29x%5E3-8, zooming in, the root of y appears to be 2.403, or something very very near it.