SOLUTION: Figure 1 represents a conical container with a diameter of 120cm and a depth of 140cm. It is filled with water to a depth of 60cm. a) Find the volume of water in the container. (S

Question 822729: Figure 1 represents a conical container with a diameter of 120cm and a depth of 140cm. It is filled with water to a depth of 60cm.
a) Find the volume of water in the container. (SOLVED)
b) Find the surface area of container in contact with the water. (SOLVED)
c)The container in Fig. 1 is inverted so that the water is now at the base of the cone with height h cm. Calculate the value of h.
* Fig. 1's cone is inverted with the tip facing down , fig
2's cone is the upright one with th base on the ground.
Appreciate your help as this is the last question for my holiday assignment. Thanks !
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The volume of a cone can be calculated as ,
where is the radius of the base and is the height of the cone.
Inside that conical container,
there is a cone of water at first,
with air above it.
When the container is inverted,
there is a cone of air on top,
and water below it.
All the cones are similar.
The radius of the conical container, is
of the height.
<--->
The ratio is the same for all the other similar cones.
Their volume is

The volume of the conical container, in cubic centimeters, is
.
The volume of water in the container, in cubic centimeters, is
.
The volume of air in the container, in cubic centimeters, is
.
We can find the height, , of the cone of air, in cm:

Once the cone is standing on its base, there is a cone of air inside the tip of the container that has a height of .
If at the tip of the cone are air, the remaining at the base of the cone are full of water.

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