The diameter of the larger circle is 12.5 cm.
The diameter of the smaller circle is 3.5 cm.
What is the approximate area of the shaded region?
A.
28.26 cm²
B.
113.04 cm²
C.
132.27 cm²
D.
254.34 cm²

- gabbyalicorn

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- gabbyalicorn

##### 1 Attachment

- gabbyalicorn

I tried to get the answer by doing \[12.5 \times 3.5 but \it turned out \to be 43.75 which was \not there. ;-; sadly\]

- gabbyalicorn

woah that was weird

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## More answers

- gabbyalicorn

@gaos

- gabbyalicorn

@pinklion23

- gabbyalicorn

@Whitemonsterbunny17

- gabbyalicorn

@geerky42

- anonymous

Area of the greater circle- area of the smaller circle
πRadius^2-πradius^2

- gabbyalicorn

6.28

- anonymous

3.14x(12.5)^2 - 3.13x(3.5)^2

- geerky42

You just need to find area of big circle and small circle using \(A = \pi r^2\)
THEN you subtract big circle by small circle.

- geerky42

First convert diameter into radius

- gabbyalicorn

how do i do that?

- geerky42

Let's just find area of bigger circle.
diameter is 12.5
So what is radius?

- gabbyalicorn

:/ radius is....a line segment that joins the center of a circle with any point on its circumference. (yes i looked it up)

- geerky42

no no I mean what is length of radius in bigger circle?

- gabbyalicorn

3.5

- geerky42

Radius is 1/2 the diameter, right?

- geerky42

So to find radius, you just divide diameter by 2

- gabbyalicorn

yes

- geerky42

So 12.5/2 = ?

- gabbyalicorn

6.25

- geerky42

Yeah, so now find area:
\(A = \pi(6.25)^2\)

- gabbyalicorn

39.25 i got kind confused on this part

- geerky42

What are you confused with?

- gabbyalicorn

just that whole part with the a= π(6.25.....etc thing

- geerky42

\(\pi\) is pi. You can use 3.14 for that.
\(etc~^2\) mean you multiply "etc" by itself
For example \(4^2 = 4\times4\)

- geerky42

Does that make sense?

- gabbyalicorn

yes

- geerky42

OK so \(A = \pi(6.25)^2\)
First, multiply 6.25 by itself

- geerky42

Then multiply it by 3.14

- gabbyalicorn

i got 122.6525

- geerky42

Good enough.
This is area of bigger circle. Keep that in mind.
Now do it again, but with smaller circle (with diameter 3.5).
Can you find area of smaller circle?

- gabbyalicorn

so replace 6.25 with 3.5

- geerky42

yeah basically.

- gabbyalicorn

kk

- gabbyalicorn

i got 38.465

- geerky42

oops forgot to convert diameter into radius

- geerky42

3.5 is diameter, so what is radius?

- gabbyalicorn

um 12.5 ?

- geerky42

No. To get radius, you divide diameter by 2.

- geerky42

So 3.5/2 = ?

- gabbyalicorn

oh 6.25

- gabbyalicorn

I dont see it as the answer ;-; i think I did something wrong

- geerky42

3.5/2 = ?

- gabbyalicorn

1.75

- gabbyalicorn

oh wow the online calculator was way off

- geerky42

Yeah. so radius is 1.75.
Now find area of circle.

- geerky42

with radius 1.75

- gabbyalicorn

1.75 x ? = ( 12.5 ) ?

- geerky42

No. \(A = \pi(1.75)^2\)

- gabbyalicorn

oh

- gabbyalicorn

9.61625

- gabbyalicorn

@geerky42

- gabbyalicorn

i guess is didn't do it right. but i double checked and it still was this answer. HELP ;-;

- gabbyalicorn

still unsure about this can you help @10115658

- anonymous

find the area of the larg circle and the small circle

- gabbyalicorn

12.5 is the area i belive

- anonymous

no, that is the diameter

- anonymous

remember, the area of a circle is
\[\pi r ^{2}\]

- anonymous

radius is half the diameter

- gabbyalicorn

6.25

- anonymous

yep, now plug it into the formula

- gabbyalicorn

3.14 x 6.25 ?

- gabbyalicorn

19.625

- anonymous

6.25^2

- gabbyalicorn

39.0625 ?

- anonymous

don't forget about the pi

- gabbyalicorn

122.65625

- anonymous

yep, now find the area of the smaller circle

- gabbyalicorn

um

- gabbyalicorn

okay, so the smaller circle is 3.5

- gabbyalicorn

so 3.14 a^2 ?

- anonymous

3.5 is the diameter, what is the radius?

- gabbyalicorn

6.25

- anonymous

no its half the diameter

- gabbyalicorn

3.125

- anonymous

no what is the diameter of the smaller circle?

- gabbyalicorn

3.5?

- anonymous

yes, and the radius is half of that

- gabbyalicorn

1.75

- anonymous

now use the formula

- gabbyalicorn

9.61625

- anonymous

correct

- anonymous

now subtract the area of the small circle from the large circle

- gabbyalicorn

113.03625

- anonymous

good job

- gabbyalicorn

so, b

- gabbyalicorn

:D yay! thank you for helping me!

- anonymous

np

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