how to find out without any info on semi circle...
may i know the source pls...
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ratio of semi circle
Source: Beat The GMAT — Problem Solving |
I originally came out at 1/2, and then some other number, but I did it the hard way and made obviously a mistake along the way. Filling in a number indeed gets me to 1/1 over as well.
At least I was right with one thing: See the two smaller circles in the larger circle.
That is why I use the name "ohwell"
At least I was right with one thing: See the two smaller circles in the larger circle.
That is why I use the name "ohwell"
Last edited by ohwell on Thu Nov 06, 2008 8:04 pm, edited 3 times in total.
but your answer is not correctohwell wrote:I come out at 1/2, thus answer D. Is this correct?
I do the following:
There are really 2 small circles in 1 big circle. The small circles have a radius of 1/4 PQ or 1/4 RS. I choose the first to go further with.
The area of one small circle is thus: Pi * (1/4PQ)^2
But we have two, so we need to multiply by 2 -> 2 * Pi * (1/4*PQ)^2
The big circle has a radius of 1/2 PQ.
The area of this bigger circle is then Pi * (1/2*PQ)^2
Finally you divide the two and you should get to 1/2.
hmm... i think i got it...
let
PQ=RS = 4
O be the centre of the circle.
diameter of one semi circle = PO=2 (radius =1)
area of one semi circle = pi r^2/2 = pi /2
Area of 4 semi circles = 4 * pi / 2 = 2 pi...(1)
Area of the circle will be = pi * r^ 2
= pi (2) ^2 = 4 pi ...(2)
Area of the shaded region = 4 pi - 2 pi =2 pi...(3)
thus ratio of area of semi circles to area of shaded region = (1) / (3) = 1/1
imo:B
wats d OA??
let
PQ=RS = 4
O be the centre of the circle.
diameter of one semi circle = PO=2 (radius =1)
area of one semi circle = pi r^2/2 = pi /2
Area of 4 semi circles = 4 * pi / 2 = 2 pi...(1)
Area of the circle will be = pi * r^ 2
= pi (2) ^2 = 4 pi ...(2)
Area of the shaded region = 4 pi - 2 pi =2 pi...(3)
thus ratio of area of semi circles to area of shaded region = (1) / (3) = 1/1
imo:B
wats d OA??
hmm... i think i got it...
let
I think U got it
nice way u solved @ it didnt make sense to me Vishu
thanks
Hi vishu,
for ease, lets take PQ=RS=4r
Let, O be the centre of the bigger circle.
radius = 2r
Area of circle = pi*4r^2
Radius of the smaller semicircle = 2r/2=r
Area of semicircle = (pi*r^2)/2
since there are 4 semicircles, total unshaded area = 2*pi*r^2
Area of shaded region = Area of circle - Area of unshaded portion
= pi*r^2(4-2) = 2*pi*r^2
Ratio of shaded portion to unshaded portion = 1:1
hope it helps.....
for ease, lets take PQ=RS=4r
Let, O be the centre of the bigger circle.
radius = 2r
Area of circle = pi*4r^2
Radius of the smaller semicircle = 2r/2=r
Area of semicircle = (pi*r^2)/2
since there are 4 semicircles, total unshaded area = 2*pi*r^2
Area of shaded region = Area of circle - Area of unshaded portion
= pi*r^2(4-2) = 2*pi*r^2
Ratio of shaded portion to unshaded portion = 1:1
hope it helps.....
let radious of the big circle be r then its area will be pi r^2.
radious of semicircle becomes (r^2)/2 and area of each smallest semicircle is
pi (r^2)/4 x1/2=pi r^2/8 ( consider 1/4(quarter of circle and within circle's quarter there is small semicircle with half of quarter's radious).
area of four small small semicircles is 4{pi r^2/8}=pi r^2/2
shaded area= (total area -white area)
(pi r^2 - pi r^2/2)=>pi r^2/2
therefore ratio of white area to shaded area is 1/1
radious of semicircle becomes (r^2)/2 and area of each smallest semicircle is
pi (r^2)/4 x1/2=pi r^2/8 ( consider 1/4(quarter of circle and within circle's quarter there is small semicircle with half of quarter's radious).
area of four small small semicircles is 4{pi r^2/8}=pi r^2/2
shaded area= (total area -white area)
(pi r^2 - pi r^2/2)=>pi r^2/2
therefore ratio of white area to shaded area is 1/1
