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

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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(20055) About Me  (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:
V = 1%2F3pir%5E2h
So we substitute 100 cubic feet for V,
and
since the diameter is 6 feet, the radius, r, is half
the diameter, or 3 feet. So we substitute 3 feet
for the radius r.
V = 1%2F3pir%5E2h
100 = 1%2F3pi%283%5E2%29h
100 = 1%2F3pi%289%29h
100 = 1%2F39pi%2Ah
Since 1%2F3 of 9 is 3,
100 = 3pi%2Ah
Divide both sides by 3pi
100%2F%283pi%29 = %283pi%2Ah%29%2F%283pi%29
100%2F%283pi%29 = h
10.61032954 = h
or the height is approximately 10.6 feet
Edwin

Answer by doukungfoo(195) About Me  (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 %28pi%29 times %28radius%29%5E2
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 %28pi%29
a=%283.14%29%283%29%5E2
a=%283.14%29%289%29
a=28.26
Now we can use the volume formula to find the height of the cone.
volume=(area of base)(height)(1/3)
100=%2828.26%29%28h%29%281%2F3%29
100=%2828.26h%29%2F3
300=28.26h
300%2F28.26=h
10.61571125=h
So a good estimate for the height of the cone shaped water tank is
10.6 feet