Awater tank in the shape of an inverted cone has a height of 11 feet and a radius of 6.0 feet. find the volume of the water tank when the water is 7 feet deep.

A water tank in the shape of an inverted cone has a height of 11 feet and a radius of 6.0 feet. The volume of water in a conical tank is 107 cubic feet.

Solution:

Consider the figure attached below as side view of inverted cone shape.  

AG = BG = 6 feet     [Radius ]

OG = 11 feet  [water tanks height ]

OE = 7 feet  [Depth of water ]

Need to calculate EC first , which is radius of uppermost surface till where the water is filled.

Consider triangle OEC and triangle OGB

Angle OEG = Angle OGB      [both are 90^{\circ}]

Angle GOB = Angle EOC  [Same angle]

So using Angle angle similarity criterion, it can be said that

Triangle OEC is similar to triangle OGB.  

  [Ratio of corresponding side of similar triangles ]

Volume of water = Volume of cone of height 7 feet and radius 42/11  feet

Formula for volume of cone =

= 106.909 which is approximately 107

Hence volume of water in a conical tank is 107 cubic feet.

c is the final : )