SOLUTION: A conical water filter has a diameter of 60cm and a depth of 24cm. It is filled to the top with water. The water filter sits above an empty cylindrical container which has a diamet

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Question 996162: A conical water filter has a diameter of 60cm and a depth of 24cm. It is filled to the top with water. The water filter sits above an empty cylindrical container which has a diameter of 40cm. The water is allowed to flow from the water filter into the cylindrical container. When the water filter is empty find the height of the water in the cylindrical container.
I know i gotta find a volume of the cone, which i got or
But i am completely stuck for the cylindrical part!
Please help! thank you!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the volume of the cone is equal to 1/3 * pi * r^2 * h

r is the radius
h is the height.
d is the diameter
the radius is equal to 1/2 tghe diameter.

you have:

d = 60 cm
h = 24 cm
r = d/2 = 30 cm

v = 1/3 * pi * r^2 * h becomes v = 1/3 * pi * 30^2 * 24 which becomes v = 7200 * pi.

that part's ok.

the volume of a cylinder is equal to pi * r^2 * h

d = diameter
r = radius
h = height

you have:

d = 40
r = d/2 = 20
h = what you want to find.
v = 7200 * pi which is the volume from the cone that's poured into the cylinder.

v = pi * r^2 * h becomes 7200 * pi = pi * 20^2 * h

simplify to get 7200 * pi = 400 * pi * h

divide both sides of this equation by 400 * pi to get:

(7200 * pi) / (400 * pi) = h

solve for h to get h = 18 cm.

the height of the water in the cylindrical container is 18 cm.

v = pi * r^2 * h becomes v = pi * 20^2 * 18 becomes v = pi * 400 * 18 becomes v = pi * 7200.

you have the same volume in the tank as the volume that was in the cylinder when the height of the water in the cylinder is 18 cm.