Question

A water storage tank has the shape of a cylinder with diameter 10 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 8 ft, what percentage of the total capacity is being used?

Answer 1

let
l= length of the cylinder 

V=πr²l r=11 Vt=(380.133)l 
x=√(121-y²) 

dv=2x dy 
10 
V=∫2l√(121-y²) dy=(373.965)l ft³ 
-11 
% of the total capacity being used=(373.965/380.133)100 
=98.38%