# Math and Arithmetic

## Math is the study of abstractions. Math allows us to isolate one or a few features such as the number, shape or direction of some kind of object. Then we can study what can be learned about the behavior of those features while ignoring everything else about the object.

###### Asked in Math and Arithmetic, Units of Measure, Volume

### How many liters are in one gallon?

1 US gallon = 3.785411784
liters.
1 Imperial (UK) gallon = 4.54609188
liters.
1 liter = 0.26417205 US gallons
1 liter = 0.21996919 Imperial (UK) gallons
Conversion to other units:
1 gallon [US, liquid] = 4 US quarts exactly
0.133681 ft3 and
128.000 fluid ounces and
0.003785 m3 and
3785.411 cm3 and
3785.411 ml
Note that a liter is constant across the world, so a US liter =
a UK, British, English, Canadian, Indian, Chinese, etc... liter.
3.785 liters per gallon.

###### Asked in Math and Arithmetic, Volume

### How are volume units related to length?

Here's all you need to know to convert between volumes (i.e. m^3
to cm^3).
Volume is distance x distance x distance. Any formula you think
about. Cube=L^3 or LxWxH, sphere is 4/3 pi x r^3 (r is distance),
cylinder = pi x r^2 x L (r x 2 and L).
Why is this? because volume extends to the 3rd dimension.
What used confuse me was when my maths teacher said that there
were 1,000,000 cm^3 in a metre cubed. I knew that 100cm were in a
metre but it confused me passed this. Thing is, that difference
becomes cubed due to it being 3rd dimension. i.e. the difference is
actually 100x100x100, i.e. 1 million.
Some other things to remember. 1 cm^3 is the same as 1
millilitre. cc actually means centimetre cubed, i.e. cm^3. As milli
means 1 thousandth there are 1000ml in a litre, therefore 1000cm^3
in a litre.
By definition, 1 cubic centimeter (cc or cm3) = 1 milliliter
= 1 mL = 1/1000 L. ("Milli" means 1/1000th.) In this way,
a standard unit of length, the meter, is directly related to a
standard unit of volume, the litre.
Thus, there are 1000 mL in a Litre, and that means that one
cubic meter = 1000 L x 1000 mL/L = 1,000,000 mL = 1,000,000 cc (or
exactly 1x106 cc), NOT 1000 cc as the previous
contributor stated.
When the previous contributor wrote about a cube, he should
have been more clear and wrote: "In the special case of a cube,
volume = (length of any side of the cube)3 since
all sides of a cube are of equal length."
In my opinion, the remainder of what the previous
contributor wrote is correct and is a good description.
If you are asking about the standard units of measure used, 1
liter is exactly 1000 cubic centimeters, and one US liquid gallon
is exactly 231 cubic inches.
If you are asking about calculating volume, that can be
determined from length measurements.
In the special case of a cube, volume = length3.
.
In all other regular objects with straight sides (prism,
pyramid, etc.) the volume will have a relationship to the length of
any particular object that depends upon the geometry of the shape.
In a rectangular prism, such as a shoe box, the volume is directly
proportional to the length of any single dimension.
.
For spherical shapes, the volume is 4/3 pi r3, where r is the
length of the radius.
For other shapes, the volume formula may be more complicated,
and for irregular shapes, the volume may have to be estimated.
.
Some irregular shapes' volumes cannot be estimated or measured
by length. The volume of a daisy flower, for example, can not
readily be measured by conventional length measurements because the
shape of the object (all those petals, stamen, stigma, filaments,
and sepals, not to mention the stem, leaves, and roots) make it too
difficult to calculate the volume by measure straight lengths.
Other methods are required to measure the volumes of such irregular
objects, including liquid displacement or three dimensional surface
scanning or tomography.

###### Asked in Scattergories and Words Starting with Certain Letters, Math and Arithmetic

### What are some math words that begin with the letter J?

A list of math terms beginning with J appears below:
Jacobi Polynomials
Jacobian (A Determinant)
Jefferson Factor
Jensen's inequality
Jet
Jeton (not related to Jet)
Join (sum of sets)
Joint Probability
Joint Variation
Jordan Canonical Form
Jordan Matrix
Jump Discontinuity
Junctions
Justification
j (used in electronics to represent the square root of -1)
Juxtaposition
junction Justify

###### Asked in Math and Arithmetic, Brain Teasers and Logic Puzzles, Algebra

### There is a bus with 7 children inside. Each child has 7 bags. Inside each bag there are 7 big cats. Each big cat has 7 small cats. All cats have 4 legs each. How many legs are on the bus?

As a riddle, the answer is zero legs on the bus since
the bus has wheels instead of legs.
But as a maths problem; It's not a tricked
question -- just a straightforward maths problem
Confirmed answer is 10990 legs.
§ Let's say the whole situation simply :
- There are 7 girls.
- Each girl has 7 backpack
- Each backpack has 7 big cats
- Each big cat has 7 little small cats.
§ Question: How many legs are there in the
bus?
§ Let's focus on each part of the question systematically,
write down on a piece of paper if you have to, following my steps
of chains.
1. Focus on the first girl first:
A B C D E F G
Girl A has 7 backpacks
2. Now focus on first backpack A1 :
A1 A2 A3 A4 A5 A6 A7
Backpack A1 has 7 big cats
3. Now focus on first big cat :
1 2 3 4 5 6 7
Ø Each big cats have 7 small cats (that's the
end of the focus)
Systematically, 7 small cats has 28 legs (7 *
4) combined with the big cat that owns this 7 small
cats.
Let's call this the "cat chain", so cat chain 1
has 32 legs altogether.
Ø So since there are 7 big cats
7 * 32 = 224 legs
Ø Therefore each backpack has 224 legs
Ø Finally, each girl has 7 * 224 = 1568
legs.
Lastly, since there are 7 girls, A to G, there are 7 * 1568
legs (per girl) = 10976 legs.
Now, since each girl also has 2 legs each;
SO, (7 * 2) + 10976 = 10990 legs altogether
Note: Disregarding bus driver, buses and etc…Only focus on the
girl and their backpacks!
Or
There are 7*7 = 49 bags and there are 7 + 7*7 = 56 cats in each
bag, meaning there are 56*4 = 224 legs in each bag. So including
the 7 children that have 2 legs each, there are 7*2 + 49(224) =
10990 legs in total.

###### Asked in Math and Arithmetic, Algebra, Area

### How much tonnage air conditioner is required for 2779 sq ft?

It depends a great deal on where you live and how well your home
is insulated. Square feet is not a great help when planning the
size of an air conditioner. It is very useful to also have the
cubic feet in the home, along with the sizes and types of
windows.
Where I live in the northwest US, a 3-ton unit would do the
trick easily, but then, we do not get the intensely hot, long
summers as you might in say, Phoenix.