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A water storage tank has the shape of a cylinder with diameter 22 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 15 ft, what percentage of the total capacity is being used?

Guest Feb 16, 2017
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From the diagram  x = sqrt(11^2 -4^2) =10.24

So the area of the shaded triangles (there are two)  =  2  x  (1/2 x 4 x 10.24)  =  40.96

Angle theta = arcsin 10.24/11 = 68.58

2 x theta =137.15   (central angle)

 

Total cross sectional area = pi r ^2 = pi 11^2 =  380.13

SECTOR area =  137.15/360 x  380.13 = 144.82 sqft

SECTOR - triangles = SEGMENT area = 144.82 - 40.96 = 103.86 sqft

 

How full is it ? 

  (Total area - SEGMENT area )/ Total area =  (380.13-103.86)/380.13 = 72.67 % full

ElectricPavlov  Feb 16, 2017

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