A water storage tank has the shape of a cylinder with diameter 14 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 13 ft, what percentage of the total capacity is being used? (Round your answer to one decimal place.)

Explanation:

Given:

The triangle ORQ is symmetric about OS as it comes from center O on the cord QR at S.

(∵ radius of the cylinder)

Now the area of triangle ORQ:

Now the angle ROS:

Therefore the reflex angle ROQ:

Now the area of sector ROQPR:

We have the area of full circle,

where:

r = radius of the circle

hence for sector:

Now the cross sectional area filled with water:

Total cross sectional area of tank:

Now the percentage of total capacity used: