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Mathematics 13 Online
zarkam21 (zarkam21):

Help please

zarkam21 (zarkam21):

OpenStudy (baru):

the steps to be followed are exactly the same as your previous question, here you have 12 m^2 as the area of the WHOLE circle

zarkam21 (zarkam21):

So \[\frac{ 180 }{ 360}\times 21^2\]

OpenStudy (baru):

yep.. assuming that 21 is a typo, it should be 12

zarkam21 (zarkam21):

72

OpenStudy (baru):

and there shouldn't be 'squared' over it

OpenStudy (baru):

\[\frac{180}{360} \times 3.14 \times r^2\] area of the the whole circle =12 so \[3.14 \times r^2 =12\]

zarkam21 (zarkam21):

3.14*12?

OpenStudy (baru):

\[area~of ~sector=\frac{180}{360} \times \color{red}{ 3.14 \times r^2}\] and \[area~of~whole~circle =\color{red}{3.14 \times r^2=12}\] so \[area~of ~sector=\frac{180}{360} \times \color{red}{12}\]

OpenStudy (baru):

just think of the formula for are of sector of a circle as: \[A= \frac{\theta}{360}\times (area ~ of ~the ~whole ~circle)\]

OpenStudy (baru):

@zarkam21 running into any trouble?

zarkam21 (zarkam21):

Yes, I just am a little confused

OpenStudy (baru):

ok, can you just tell me the formulas for 1. area of a circle 2. sector of a circle (the formula in general, we are not discussing this specific question)

OpenStudy (baru):

let radius=r and angle=\(\theta\)

zarkam21 (zarkam21):

sooooo 180/360 *12

OpenStudy (baru):

yep, for this question... if you tell me exactly which part is bothering you, i can try explaining.

zarkam21 (zarkam21):

The part that is bothering me is when they already give you the area, I get confused then

OpenStudy (baru):

do you understand these formula? \[area~of~full~circle= 3.14 \times r^2\] and \[~area ~of ~sector~=\frac{\theta}{360} \times 3.14 \times r^2\]

OpenStudy (baru):

'r' is the radius of the circle and \(\theta\) is the angle of the sector.

zarkam21 (zarkam21):

And if they give you the diameter insteead, you would just divide that by 2 right

OpenStudy (baru):

yes

OpenStudy (baru):

\[area~of ~sector=\frac{\theta}{360} \times \color{red}{ 3.14 \times r^2}\] observe how the part of the formula marked in red, is the formula for area of a full circle

OpenStudy (baru):

so we can just re-write the formula as\[area~of ~sector=\frac{\theta}{360} \times \color{red}{ area~of~full~circle}\]

zarkam21 (zarkam21):

Now for this one,

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