Question 1137779: Hello all, if anyone can assist me in setting up and solving this problem, I would be grateful.
The volume of a can is directly proportional to the height of the can. If the volume of the can is 700cm cubed when its height is 15.62 cm, find the volume to the nearest whole number of a can with height 17.96 cm.
The volume of the can is ______when the height is 17.96 cm.
Thank you!
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39613)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! direct variation formula is y = k * x.
let v = y and x = h and the formula becomes v = k * h
when v = 700 and h = 15.62, then solve for k to get k = (700 / 15.62) = 44.81434059.
that's your constant of variation.
when h = 17.96, then v = 44.81434059 * 17.96) = 804.865557.
that would be 805 cubic cm rounded to the nearest whole number.
in fact, in this problem, k is equal to the area of the base of the can.
that doesn't change, so it becomes the constant of variation.
the volume of the can is equal to the area of the base * the height.
if the volume is 700 cubic cm and the height is 15.62 cm, then you can solve for the area of the base to get 700 / 15.62 = 44.81434059 square cm.
apply that same area of the base to the new height and you get 805 cubic cm rounded to the nearest whole number.
since they're directly proportional, you could even have done as follows>
15.62 / 700 = 17.96 / x
cross multiply to get 15.62 * x = 700 * 17.96
solve for x to get = 700 * 17.96 / 15.62 = 805 rounded to the nearest whole number.
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