Question 484652: Daughter and I are studying for ACT. Stuck!!!! This question does not belong in this area but we couldn't find anything related to ratios.
Volume of a cone
The formula for the volume of a cone is V= 1/3(pi)(r^2)(h) If the radius is doubled and the height is divided by 3, what will be the ratio of the new volume to the original volume? (Is this is a trick? New to Old?)
The answer is 4:3.
We are not understanding how to get to this. We can plug numbers into the formula and get to the answer They show a series of equalities (hopefully the right term) and give no info on how they are reducing the formula. Here is our attempt at typing what is written as an answer.
V1= new volume r1=new radius h1=h/3
V1 = 1/3(pi)(r1^2)h1 = 1/3(pi)(2r^2)(h/3) = 4/9(pi)(r^2)h = 4/3V so the ratio
V1:V = 4:3
We absolutely appreciate any help we can get.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Instead of using all these variables (V1, V, R1, R, h, h1), just use V, V1, r, and h. The volume of the original cone is
and the volume of the new cone is
^2 \frac{h}{3})
 = \frac{4}{3}V)
Hence the ratio of the new volume to the original volume is (4/3)V : V, or 4/3:1 = 4:3.
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