Amount - Gallons in Tank

[Guest]

The problem and its solution has been fairly well described so far......what is it that is not clear.....???
If you have a specific question...then ask it....deal with the problem as a series of steps.....and solve each step along the way.

The problem ..... a tank 25 ft long, horizontal, circular crossection, diameter is 5 ft, so radius is 2.5ft.
There is some oil in the tank, 15 inches deep OR 1.5 ft deep. It forms a segment of a circle at the bottom of the tank
We are tasked to find the area of this segment, multiply by length of tank, and convert to gallons.

In finding a solution we use the fact that the segment of oil together with 2 radii (forming a triangle) from the centre of the circle forms a sector of the circle. First we find the area of the sector of the circle, then subtract off the triangle bit to give the area of the segment
Then multiply by length and convert to gallons.

To determine what level of oil is in the tank we dip it to find its depth.
We now know the depth of the segment of oil and the radius of the circle so we can find the other dimensions needed to calculate the area.
And we have shown several methods of doing that in previous posts......simplifying it down to basic geometry and trigonometry.....

[Guest]

I don't understand - chord, arc, hypotenuse, radians.

I still don't understand - sector, segment.

"The problem ..... a tank 25 ft long, horizontal, circular crossection, diameter is 5 ft, so radius is 2.5ft.
There is some oil in the tank, 15 inches deep OR 1.5 ft deep. " I understand this part.


I still don't understand the remainder of solution.

It's ok - you don't have to explain further. I just won't understand it.

[Guest]

You can explain further if you'd like.

[Guest]

Please reply - thanks.

[Guest]

Please respond - thanks again.

[Guest]

I don't understand - chord, arc, hypotenuse, radians.

A chord is a straight line cutting straight across a circle any where, If it cuts straight across the centre then it is the diameter
An arc is a curved part of the circumference.
Hypotenuse is the sloping side of a right angled triangle, It is the side opposite the rightangle.
Radians are the unints to measure the size of angles. You can also measure the size of a angle in degrees. There are 360 degrees in a complete circle and 180 degrees in a semicircle and 90 degrees in a right angle. There are 2 x Pi radians is a complete circle and Pi radians in a semicircle and Pi / 2 radians in a right angle. So the means 180 / Pi = 180 /3.142 = 57.3 degrees in 1 radian.


I still don't understand - sector, segment. .... A sector is part of a circle, sort of like a triangle with a curved side. It is like a slice of an apple tart or a slice of a Pizza. It has a triangular bit bounded by 2 radii from the centre and a chord and a segment bit bounded by an arc and a chord.
A segment is a slice cut straight across a circle, bounded by a chord (the cut line) and a curved arc ( part of the circumference )


"The problem ..... a tank 25 ft long, horizontal, circular crossection, diameter is 5 ft, so radius is 2.5ft.
There is some oil in the tank, 15 inches deep OR 1.5 ft deep. " I understand this part. ....This should read 15 inches deep OR 1.25 ft deep.
There are 12 inches in a foot..... and 15 - 12 = 3 inches = 0.25 ft or 1/4 of a foot.

[Guest]

Thanks for additional info - I am learning more.