A water 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.

Answer: 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.  [tex]\frac{\mathrm{OE}}{\mathrm{O} \mathrm{G}}=\frac{\mathrm{EC}}{\mathrm{GB}}[/tex]   [Ratio of corresponding side of similar triangles ] [tex]\frac{7}{11}=\frac{E C}{6}[/tex][tex]\mathrm{EC}=\frac{42}{11} \text { feet }[/tex] Volume of water = Volume of cone of height 7 feet and radius 42/11  feet Formula for volume of cone = [tex]\pi r^{2} h=\pi \times\left(\frac{42}{11}\right)^{2} \times \frac{7}{3}[/tex] = 106.909 which is approximately 107Hence volume of water in a conical tank is 107 cubic feet.