ac is the diameter. Calculate the area of sector (to the nearest whole number) created by cbd .

Question

ac is the diameter. Calculate the area of sector (to the nearest whole number) created by cbd    .

undeaddragon26 · Answer

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undeaddragon26 · Answer

@e.mccormick

tanya123 · Answer

Asector=n∘360∘πr2

Where n is the degree measure of the central angle of the sector and of the arc, and r is the radius.
r = d/2

undeaddragon26 · Answer

im confused

tanya123 · Answer

Sorry, can't explain ha ha ha :)

e.mccormick · Answer

One way to think of it is you are looking at a percentage of the area of a circle.  How this percentage is found is through a ratio of the angles.

e.mccormick · Answer

Let me explain this with an easy one, $90^\circ$.  It is a good example because you know that $90^\circ$ is one quadrent or one quarter of a circle.

So my ratio would be $\dfrac{90^\circ}{360^\circ}$  Well, if you simplify...

$\dfrac{90^\circ}{360^\circ}$

$\dfrac{9^\circ}{36^\circ}$

$\dfrac{9^\circ}{9^\circ\cdot 4}$

$\dfrac{1}{4}$

So I end up with the same quarter!

If instead of 90, you put in the degree measure of your arc, it will give you the fraction of the circle's area that is the arc's area.

undeaddragon26 · Answer

so 1/4?

e.mccormick · Answer

For 90 is is 1/4 the area of the circle.  Your is not 90.  Is that 30 the arc measure?

undeaddragon26 · Answer

what

e.mccormick · Answer

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undeaddragon26 · Answer

oh so whats the answer i get it and i did the math but idk whats the right answer

e.mccormick · Answer

Well, is that 30 degrees?  That is what I am trying to clarify.

undeaddragon26 · Answer

yea

e.mccormick · Answer

OK, so you need the area of the whole circle, then multiply it by $\dfrac{30}{360}$ because that is the portion of the circle you are interested in.  You don't want the area of all 360 degrees in the circle, so you divide out the 360 to get the are of 1 degree.  Then you multiply by the number of degrees of are you want, which is 30 in this case.

e.mccormick · Answer

Well, what did you set up for the area of the whole circle?

e.mccormick · Answer

With that 16 there, which I do not know if that is the radius or the diameter, it is going to be more than that.

Area of a whole circle:

$A=\pi r^2$

Area of an arc of s degrees:

$A=\dfrac{s}{360}\cdot \pi r^2$

undeaddragon26 · Answer

so whats the answer

undeaddragon26 · Answer

bc im lost

e.mccormick · Answer

You just did the percentage part, the .08333333333333333333 thing.  You need to multiply that by the area of the whole circle.  That is just the percentage or ratio that is needed to convert the area of the whole into the area under the arc.

undeaddragon26 · Answer

so that number times 360

e.mccormick · Answer

No.  .08333333333333333333 times the area of the whole circle.  Or .0833 for a good enough approx.