SOLUTION: A bucket full of water is in the form of a frustum of a cone. The bottom and top radii of the frustum are 18cm and 28cm respectively and the vertical depth is 30cm. If the water in

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Question 1033020: A bucket full of water is in the form of a frustum of a cone. The bottom and top radii of the frustum are 18cm and 28cm respectively and the vertical depth is 30cm. If the water in the bucket is then poured into an empty cylindrical container with base radius 20cm, find the depth of the water in the container. (Take pie=22 over7
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
V frustum of cone =
Volume of a conical frustum: ◦V = (1/3) * π * h * (r1^2 + r2^2 + (r1 * r2))
r1=18
r2=28
height = 30
V = %281%2F3%29+%2Api+%2A+30%2818%5E2+%2B28%5E2+%2B18%2A28%29
=50642.5 in^3
Volume of cylinder = 1/3 pi r^2h
50642.5 = (1/3) *pi*20^2*h
h= 50642.5*3/ (pi*20^2)
= 120.9 inches

Answer by ikleyn(53646) About Me  (Show Source):
You can put this solution on YOUR website!
.
A bucket full of water is in the form of a frustum of a cone. The bottom and top radii of the frustum are 18cm and 28cm
respectively and the vertical depth is 30cm. If the water in the bucket is then poured into an empty cylindrical container
with base radius 20cm, find the depth of the water in the container. (Take pie=22 over7
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        The solution in the post by @mananth is incorrect, both fatally and cosmetically.
        The fatal mistake is where @mananth calculate the volume of the cylinder as (1/3)*pi*r^2*h.
        The cosmetic mistake is where @mananth uses inches instead of centimeters.

        I came to bring a correct solution.


Volume of a conical frustum: V = = 16120%2Api cm^3.

Volume of cylinder = pi*r^2h

16120%2Api = pi%2A20%5E2%2Ah

h = 16120%2F20%5E2 = 40.3 cm.         ANSWER

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A note specially for the creator of this problem


        Notice that the value of pi is canceled in both sides of the equations.
        Therefore, the precise value of pi does not matter in this problem.

        So, do not worry about things that do not have any matter and do not play any role.