+0

# 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

+5
326
1

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
Sort:

#1
+10614
0

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

### 2 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details