12. 6 Areas of Circles and the Number PI
what is the circle area formula
a circle of radius r units has area A square units, where A = π(r)^2
the greek letter pie stands for
a mysterious number that is approximately equal to 3.14159. since at least the time of the ancient babylonians and egyptians, nearly 4000 years ago, people have known about, and been fascinated by, the remarkable number pie
why does the circumference of a circle divided by the diameter always result in the same number
every circle is a scaled version of one fixed circle. in scaling, both the circumference and diameter are multiplied by the same number, thus when the circumference is divided by the diameter, the same value results for all circles
what is the area of a circle
familiar formula: A = π(r)^2 for the area A in square units of a circle of radius r units
for any circle whatsoever...
the circumference divided by the diameter is always equal to the same number; this number is called pi and is written with the greek letter (π)
what's the formula to obtain pie
π= circumference divided by diameter
ex: if you plan to make a circular garden with a radius of 10 ft and you want to enclose the garden with a fence, then you will need
2π x 10ft = 63 ft approximately
if a unit of length measurement has been chosen , and if D is the diameter of a circle of radius r units, and C is its circumference, then
D= 2r
explain how to use the circle area formula correctly
be sure that you square only the value of r, and not the value of π(r) if you multiply π x r first, and then square the result, your answer will be π times too large
what are the two circumference formulas
c = π(D) c= 2π(r)
what's the formula to obtain circumference of a circle
circumference = π x diameter
what's the diameter of a circle
distance across the circle through the center (double the radius)
what's the radius of a circle
distance from the center of the circle to any point on the circle
ex: suppose we want to find the area of a circular patio of diameter 30 ft.
if the diameter is 30 ft, then the radius is 15 ft, and the area of the patio is (apply area formula)
experiment to determine the approximate value of π
take a sturdy cup, can, or plate; measure the distance around the rim with a tape measure; and measure the distance across the cup, can or plate, at the widest part. when you divide these numbers you get an approximate value for πif the rim of the cup, can or plate is a circle. But even with a big plate, an accurate tape measure, and careful measuring, you will probably be able to determine only that π is about 3.1.
what's circumference of a circle
the distance around the circle;
how do we know the decimal expansion of the number π
there are many known formulas for π, and these formulas can be used to find the decimal representation of π.....
if you enter π on your calculator you will see many more decimal places....
your calculator can show only a finite number of digits behind the decimal point, but it turns out that the decimal expansion of π goes on forever and does not have a repeating pattern
what is one elegant formula for π
π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ..... this equation was discovered by Indian mathematicians in the 15th century..the ellipses in the expression to the right of the equal sign indicates that this expression goes on forever, continuing the pattern of adding and subtracting fractions whose denominators are the odd numbers in sequence...