Circles And Anglesmath Problem Solving

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Grade 2 Math Problem Solving
Vertical Angles Problem Solving
Steps In Math Problem Solving
Circles And Angles Math Problem Solving Worksheets
Circles And Angles Math Problem Solving Solver

Draw a circle with a diameter (all the way across the circle) of 1

Then the circumference (all the way around the circle) is 3.14159265... a number known as Pi

The formula for circumference is C = 2πr C = 2 π r The formula for area of a circle is A =πr2 A = π r 2 Remember, that we approximate π π with 3.14 3.14 or 22 7 22 7 depending on whether the radius of the circle is given as a decimal or a fraction.
Problem 1: The diameter of a cart wheel is 2.1 m. Find the distance traveled when it completes 100 revolutions. Solution: In order to find the distance covered in one revolution, we have to find the circumference of the circle.
Microsoft Word - Problem Solving Circle.docx Created Date: 3:03:37 PM.

Pi (pronounced like 'pie') is often written using the greek symbol π

The definition of π is:

The Circumference
divided by the Diameter
of a Circle.

The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is!

To help you remember what π is ... just draw this diagram.

Finding Pi Yourself

Draw a circle, or use something circular like a plate.

Measure around the edge (the circumference):

I got 82 cm

Measure across the circle (the diameter):

I got 26 cm

Divide:

82 cm / 26 cm = 3.1538...

That is pretty close to π. Maybe if I measured more accurately?

Using Pi

We can use π to find a Circumference when we know the Diameter

Circumference = π × Diameter

Example: You walk around a circle which has a diameter of 100 m, how far have you walked?

= π × 100 m

= 314 m (to the nearest m)

Also we can use π to find a Diameter when we know the Circumference

Diameter = Circumference / π

Example: Sam measured 94 mm around the outside of a pipe ... what is its Diameter?

= 94 mm / π

= 30 mm (to the nearest mm)

Radius

The radius is half of the diameter, so we can also say:

For a circle with a radius of 1

The distance half way around the circle is π = 3.14159265...

Digits

π is approximately equal to:

Grade 2 Math Problem Solving

3.14159265358979323846…

The digits go on and on with no pattern.

π has been calculated to fifty trillion decimal places and still there is no pattern to the digits

Approximation

A quick and easy approximation for π is 22/7

22/7 = 3.1428571...

But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.

A really good approximation, better than 1 part in 10 million, is:

355/113 = 3.1415929...
(think '113355', slash the middle '113/355', then flip '355/113')

Summary:

22/7	=	3.1428571...
355/113	=	3.1415929...
π	=	3.14159265...

Remembering The Digits

I usually just remember '3.14159', but you can also count the letters of:

'May I have a large container of butter today'
3 1 4 1 5 9 2 6 5

To 100 Decimal Places

Here is π with the first 100 decimal places:

3.14159265358979323846264338327950288
4197169399375105820974944592307816
4062862089986280348253421170679...

Calculating Pi Yourself

There are many special methods used to calculate π and here is one you can try yourself: it is called the Nilakantha series (after an Indian mathematician who lived in the years 1444–1544).

Vertical Angles Problem Solving

It goes on for ever and has this pattern:

3 + 42×3×4 − 44×5×6 + 46×7×8 − 48×9×10 + ...

(Notice the + and − pattern, and also the pattern of numbers below the lines.)

Steps In Math Problem Solving

It gives these results:

Term	Result (to 12 decimals)
1	3
2	3.166666666667
3	3.133333333333
4	3.145238095238
...	... etc! ...