MHB Circumference and Area of A Circle

[susanto3311]

hello expert...

How to find the circumference of a circle and area of a circle quickly?
it's possible using method like ratio or series like pythagoras theory (3,4,5).
or another way?

somebody could help me out?

cheers...
susanto3311

 

[MarkFL]

What do you know about the circle?

 

[SuperSonic4]

You can find both using the radius (or diameter) of the circle. The main way to find them is also the quickest way

 

[susanto3311]

hi guys...

i want to easy find area & circumference of circle to multiple choice exam with "tactics & logic" approach, again like triagle phytagoras concept just know 3,4 the last result must be 5..

 

[SuperSonic4]

I'm still not 100% sure what you're asking. I get the impression you want to know a way of finding the area of a circle without having to work it out in the same way that if you know two sides of a right angled triangle are 3 and 4 then the third must be 5.

If so then the only real shortcut is to learn the results. I would also use exact answers (left in terms of $$\pi$$) as it's both easier to work out and correct (not an approximation).

In multiple choice it may be worth saying $$\pi \approx 3$$

---

If you're given the diameter instead of the radius then you can use these formulae:

[math]C = \pi d[/math] and $$A = \frac{\pi}{4} d^2 $$ where $$d$$ is the diameter.

Just remember not to use that approximation too much...
[youtube]V98soOyQWKY[/youtube]

 

[susanto3311]

hello guys...

I found the nearest value of area of the circle with a simple trick using vedic maths..

please, read this link http://vedicmathstricks.yolasite.com/

how do make formula for find the nearest value of circumference of the circle?

any ideas?

thanks...

 

[MarkFL]

It appears to me what is being done there is to use 22/7 as an approximation for $\pi$ (I recall using this approximation in primary school). If you require more decimal places, then you can use 355/113.

 

[susanto3311]

hello guys...

I found the nearest value of area of the circle with a simple trick using vedic maths..

please, read this link http://vedicmathstricks.yolasite.com/

how do make formula for find the nearest value of circumference of the circle?

any ideas?

thanks...

using vedic method, how to find easy radius? i mean simple calculation..

 

[MarkFL]

If we are given the area $A$ of a circle, or the circumference $C$, then using the rational approximation:

$$\pi\approx\frac{22}{7}$$

then we find:

$$A\approx\frac{22}{7}r^2\implies r\approx\sqrt{\frac{7A}{22}}$$

$$C\approx2\cdot\frac{22}{7}r\implies r\approx\frac{7C}{44}$$