Surface Area and Volumes

Surface Area and Volumes


Surface area is the measure of how much exposed of area a solid object has, expressed in square units.General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century.

Definition of Surface Area:

While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a lot of care. Surface area is an assignment

of a positive real number to a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the surface area is its additivity: the area of the whole is the sum of the areas of the parts. More rigorously, if a surface S is a union of finitely many pieces S₁, …, S_r which do not overlap except at their boundaries then

LEARNING FRACTIONS

The study of Fractions is an important topic under Math. Fractions are basically a type of numbers. There are different types of numbers:

• Whole Numbers
• Natural Numbers
• Integers
• Fractions
• Rational Numbers
• Irrational Numbers

Fractions are those numbers which are represented as the 'parts of a whole' . For example: 1/4 is one part out of four total parts. Students can learn how to compare fractions and understand the steps involved.

Various mathematical operations can be conducted on Fractions. Students can learn :

• How to add fractions
• How to subtract fractions
• How to divide fractions
• How to multiply fractions

To work with ease with Fractions, students have to learn:

• How to solve complex fractions
• How to simplify a fraction
• How to convert fractions into other forms of numbers

Based on the knowledge of all the above mentioned operations, students can learn how to solve fractions.

Math graphed equation

Welcome to free math tutor,

If you've graphed equations, look at the graph
of y=1/x. If you look at the region enclosed by y=1/x, the line y=0 (the
x-axis), and the lines x=1 and x=e, it looks like a rectangle but with one
curved side. What is the area of this shape? In fact, it is exactly 1. examples on math help;
Mathematically speaking, we say "the area under the curve y=1/x from 1 to e
is 1," or even better, "the *integral* of 1/x from 1 to e is 1." This is
because if we replaced the line x=e with some line x=b for some b>1, the
area of the region is the natural logarithm of b.

Note the natural logarithm
of e is 1, because e^1 = e; that is, 1 is the exponent for which the base
(e) is equal to e.

And finally, for something I hope someone else will explain,

e^(i*Pi) = -1, where i is the square root of -1.

Solving the math equations

Welcome to math help com,

The equations that describe what happens to any one part are not very
difficult to write down, but solving the equations for all of these
parts at the same time would be extremely time-consuming. That is why
this type of modeling is almost always done using a computer.

The computer solves the mathematical equations, the computer scientists
programmed the equations into the computer, examples on free math;
but (pay attention here) the engineers had to write down the equations in
the first place. For that, they needed to know a lot of mathematics, especially calculus
and differential equations. learn more on math forum.

Math related construction

Welcome to free math tutoring,

suppose you were designing a concrete freeway over-pass.
One of the things you would need to understand is how the concrete
cures as a function of time. similar exercise on free math
How long does one 'batch' need to cure
before construction can continue? When does it need to be tested?
How long until the bridge can be opened to regular traffic? (Concrete
appears to 'dry' in a day or two, but actually does not reach its full
strength for over a month!)

Well, it turns out that the strength of
the concrete as a function of time is described by an equation of the
form S=c(1-e^-kt) where S is the strength at time t and c and k are
constants specific to the type of concrete you are using. (How strong
is the concrete at time t=0? How strong is it as t approaches
infinity? How long will it take to get to half of its final
strength?) more examples on free math help.

Math practice

Welcome to free math tutor online,

One final thing you need to learn is the importance of _practicing_
what you've learned. The more you practice the material at each stage,
the more quickly you'll be able to learn the material at the next
stage. Think of practice as a pain management game. free math; A little pain up
front is often the key to avoiding a lot of pain later on. (If you
think about it, the main task of becoming an adult is learning, and
applying, that lesson.)

I know this advice sounds almost too simple to be useful. But I can
assure you that almost everyone who has become any good at math has
learned it in this way.

And whenever you come across a particular problem that you can't
solve, write to Dr. Math, and we'll see what we can do to help you get
past whatever's blocking you. more explanation on math forum.

Math Interesting

Welcome to free math tutoring online,
We get this question all the time, and here are a few of the answers
that I've given in the past. I'm sorry if they seem long, but it's an
important question, and I've put a lot of thought into the answers. I
hope you can get something out of at least one of them.


1) Here is one of my favorite stories (from _The Little, Brown Book of
Anecdotes_):

At Columbia University, the young professor Raymond Weaver gave his
first class in English literature their first quiz. more examples on math tutoring;
The young men,
who had been trying to make things hard for the new instructor,
whistled with joy when Weaver wrote: "Which of the books read so
far has interested you least?" They were silent, however, when he
wrote the second, and last, question: "To what defect in yourself
do you attribute this lack of interest?"

Math _is_ interesting, and once you've figured out that it's
interesting, it's the easiest thing in the world, and more fun than
baseball or video games or going to the movies. more on free math.