SOLUTION: A hollow container consists of a cylinder with a cone on top The container contains oil up to the level of the top of the cylinder. the container is then turned upside down. Fi

Question 866755: A hollow container consists of a cylinder with a cone on top
The container contains oil up to the level of the top of the cylinder. the container is then turned upside down. Find the depth of the oil
Hight of cylinder = 6cm
width = 8cm
and hight of cone = 4cm
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A hollow container consists of a cylinder with a cone on top.
The container contains oil up to the level of the top of the cylinder.
the container is then turned upside down.
Find the depth of the oil.
;
height of cylinder = 6cm
width = 8cm, radius = 4cm
and height of cone = 4cm
:
Find the vol of the cylinder, this is also the vol of the oil

V = 301.59 cu/cm
:
Find the vol of the cone.

V = 67.02 cu/cm
:
Find the vol of the oil in the cylinder, when the cone is full
301.59 - 67.02 = 234.57 cu/in
:
Let h = the height of the oil in the cylinder

h =
h = 4.67" height in the cylinder
then
4.67 + 4 = 8.67" height of the oil in the container when cone is down

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
volume of the cylinder is equal to pi * r^2 * h
h = 6 = height of cylinder.
d = 8 = diameter of cylinder.
r = 1/2 * 8 = 4 = radius of base of cylinder.
v = pi * 4^2 * 6 = 96 * pi = 301.5928947.

volume of the cone is equal to 1/3 * pi * r^2 * h
h = 4 = height of the cone.
r = 4 = radius of the base of the cone.
v = 1/3 * pi * 4^2 * 4 = 64/3 * pi = 67.02064328.

when you invert the cylinder, the oil rushes into the cone and fills it up.

Since the volume of the cylinder is larger than the volume of the cone, there will be oil left over after the cone is full.

that left over oil goes into the cylinder.

the volume of oil that is left over is equal to 301.5928947 - 67.02064328 which is equal to 234.5722515.

this is the volume of oil that is now in the cylinder.

the equation for the volume of the cylinder is:

v = pi * r^2 * h

pi stays the same at 3.141592654 and r stays the same at 4.
v becomes 234.5722515 which is the volume of the oil that is now in the cylinder.
since v = 234.5722515 and r = 4, the formula for the cylinder becomes:

234.5722515 = pi * 4^2 * h

you want to solve for h.

you get h = 234.5722515 / (16*pi).

solve for h to get:

h = 4.6666..... which is equal to 4 2/3.

that should be your answer.

confirm by adding up the volume in the cone and the volume in the cylinder.

volume in the cone is equal to (1/3) * pi * 4^2 * 4 = 67.02064328
volume in the cylinder is equal to pi * 4^2 * 4.6666... = 234.5722515
total volume in cone and cylinder is equal to 301.5928947.

since this is the original volume of the oil in the cylinder before you turned the cylinder upside down, the value of h = 4 and 2/3 is good.

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