Posted by **Anonymous** on Saturday, December 8, 2012 at 11:59am.

How many gallons of gas is in a cylindrical tank (that is laying on it’s side, the circular bases are vertical, the diameter of the bases are 5 feet, the length of the tank is 8 feet, the gas is at a 2 ft level)?

- pre calculus -
**Reiny**, Saturday, December 8, 2012 at 12:57pm
Draw a cross-section of the ends of the cylinder

The level of gas will form a segment of the circle, the chord being .5 ft from the centre of the circle.

Volume = area of segment x 8

to find the area of the segment, you can use formulas found in several websites, or just find it analytically

If you join radii to the ends of the chord, we have a sector.

let's find the central angle of that sector.

cosØ = .5/2.5 = .2

Ø = 78.46

so the central angle is 156.96 °

Length of chord = 2(2.5sin78.6) = 4.899

area of triangle within the sector = (1/2)(4.899)(.5) = 1.22474

area of whole circle = 2.5^2π = 19.635

area-of-sector/19.638 = 156.96/360

area of sector = 8.55899

area of segment = 8.55899 - 1.22474 = 7.33425

volume of gas in tank = 8(7.33425) = 58.674 gallons

check my arithmetic.

Nice question. I used to add a part b) to this which said.

Suppose the cylinder is turned on its end, how high will the level of gas be in the tank?

## Answer this Question

## Related Questions

- calculus - How many gallons of gas is in a cylindrical tank (that is laying on ...
- math - A cylindrical tank is lying horizontally on the ground, its diameter is ...
- Math - A cylindrical tank with radius 6 in. and length 12 in. is placed on its ...
- Math - A cylindrical storage tank has a height of 100 feet and a diameter of 10 ...
- Math - A cylindrical storage tank has a height of 100 feet and a diameter of 10 ...
- Calculus - Find volume of cylinder - There is a cylindrical tank lying ...
- GEOMETRY - A cylindrical tank if 8 ft. in diameter and 20 ft tall. how many ...
- CALCULUS - A cylindrical oil storage tank 12 feet in diameter and 17feet long is...
- College Physics - How many gallons of Oil would be in a cylindrical tank that ...
- Calc - A cylindrical slime tank is placed so that the axis of the cylinder is ...