SOLUTION: a water tank in the shape of a cone holds 100 cubic feet of water and has a diameter of 6 feet. estimate its height

Question 100565: a water tank in the shape of a cone holds 100 cubic feet of water and has a diameter of 6 feet. estimate its height
Found 2 solutions by Edwin McCravy, doukungfoo:
Answer by Edwin McCravy(6932) (Show Source):
You can put this solution on YOUR website!
a water tank in the shape of a cone holds 100 cubic feet of water and has a diameter of 6 feet. estimate its height

The volume of a cone is given by the formula:
=
So we substitute cubic feet for ,
and
since the diameter is feet, the radius, , is half
the diameter, or feet. So we substitute feet
for the radius .
=
=
=
=
Since of is ,
=
Divide both sides by
=
=
=
or the height is approximately feet
Edwin

Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website!
The volume of a cone is equal to area of the base times the height times 1/3
The base of a cone is a circle.
Area of circle equals times
To use this formula we need the radius but all that is given is the diameter
so to find radius just divide diameter by 2
6/2=3
The radius is 3 feet.
Now we can find the area of the base. Use 3.14 for

Now we can use the volume formula to find the height of the cone.
volume=(area of base)(height)(1/3)

So a good estimate for the height of the cone shaped water tank is
10.6 feet