dave13 wrote:

reto wrote:

Bunuel wrote:

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

(A) 4

(B) 3

(C) 2

(D) \(\sqrt{3}\)

(E) \(\sqrt{2}\)

Kudos for a correct solution.Attachment:

2015-10-22_0821.png

Plug in some values for the the whole circle. I took r = 4. Which means, the whole circle has area of 16*pi

which equals 4x of the area.

So the shaded region is 3x,

hence 12pi and the small region is 4pi. Therefore the small circle has radius 2 and diameter 4pi.The large circle has diameter 8pi because i picked initially 4 as the radius (2*r = 8).

Hence the large circumference is double the small one. Answer C.

Hi

pushpitkc,

i am trying to understand the above solution

if radius = 4 and the whole circle area is 16*pi how can it be equal to 4x ??

also how can shaded region area be 3x ? somehow cant wrap my mind around this this

is it " hence 12pi and the small region is 4pi" 12 pi is it area

and what about 4pi

morever, when i read question stem " if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?"

i undestand it like this

pi*r^2 = area of circle

2pi *r = circimference of circle

let area of larger non shaded region is 6

then if if the area of the shaded region is 3 times the area of the smaller circular region, then area of smaller is 2, because 2 goes into 6 three times... this is just a first idea solution that came to my mind

have a great weekend

Hey

dave13To understand the part about the circle having an area 4x, you will have to

take a look at the question which states that "area of the shaded region is 3

times the area of the smaller circular region"

We are assuming the smaller circle to have area x. Since the shaded region

has 3 times the area, making the area of the shaded region 3x. Now, the area

of the circle which contains the small circle and the shaded region will have an

area of x+3x = 4x

Once that part is clear, hope you understood the flaw in your reasoning!

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