geometry
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sibbineni
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If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?
Let A be the area of circle A
Let B be the area of circle B
Let Y be the area of SquareWXYZ
let x be the side of the square
area of squareWXYZ=x^2
given that
A=3B---(1)
B=1/6Y---(2)
to find the ratio of area of a circle inscribed within WXYZ to that of the area of circle A?
The side of square 'x' becomes the diameter of the circle
so the radius of inscribed circle is x/2
area of the inscribed circle is ∏r^2
=∏(x/2)^2=∏x^2/4---(3)
from (1)
A=3B
=3*1/6Y
since Y=Area of square =x^2
=1/2x^2 ---(4)
(3)/(4)==>∏x^2/4/1/2x^2 ==>∏/2
IMO C
Let A be the area of circle A
Let B be the area of circle B
Let Y be the area of SquareWXYZ
let x be the side of the square
area of squareWXYZ=x^2
given that
A=3B---(1)
B=1/6Y---(2)
to find the ratio of area of a circle inscribed within WXYZ to that of the area of circle A?
The side of square 'x' becomes the diameter of the circle
so the radius of inscribed circle is x/2
area of the inscribed circle is ∏r^2
=∏(x/2)^2=∏x^2/4---(3)
from (1)
A=3B
=3*1/6Y
since Y=Area of square =x^2
=1/2x^2 ---(4)
(3)/(4)==>∏x^2/4/1/2x^2 ==>∏/2
IMO C
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missionmba
- Master | Next Rank: 500 Posts
- Posts: 288
- Joined: Thu Jul 31, 2008 10:54 pm
- Location: Bombay, India
2008 wrote:If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?
A. ∏/12
B. ∏/6
C. ∏/2
D. 2∏
E. √12∏[/img]
Let circle B has area 6
then A has area 18
and sq WXYZ has area 36 => Side of square = 6.
Now, area of circle insribed in square with side 6 = ∏(D/2)^2 = 9∏
Finally, ratio of the area of a circle inscribed within WXYZ to that of the area of circle A =
9∏/18 = ∏/2
Much easier way to solve i guess
Mission Mba
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