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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