# Thread: Calculating percentage capacity used...help!!!

1. ## Calculating percentage capacity used...help!!!

The problem is:

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 12 ft, what percentage of the total capacity is being used?

I'm having a bit of trouble figuring this out...please help!

2. Originally Posted by DarthPipsqueak
The problem is:

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 12 ft, what percentage of the total capacity is being used?

I'm having a bit of trouble figuring this out...please help!
The area of the circular cross section is $A=\pi(11)^2$

If we impose coordinate axes at the center of the of the circle, then the area over which the water covers is

$2\int_{-11}^1\sqrt{(11)^2-y^2}dy$

So, %= $\frac{200\int_{-11}^1\sqrt{(11)^2-y^2}dy}{\pi(11)^2}$

3. You can calculate angle A on the attachment from

$SinA=\frac{1}{11},\ A=Sin^{-1}\frac{1}{11}$

Then calculate the volume within the sector of angle $180^o+2A$

Then calculate the area of the triangle with angle $90^o-A$

using $area=0.5(1)(11)Sin(90-A)$.

Double this, add the result to the sector area and divide by $\pi(11)^2$

to find the ratio, then multiply by 100 for the percentage.

You could also calculate the area of the upper sector.

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### calculate capacity in to percentage

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