geometry

[2008]

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]

[2008]

OA is C

[raunekk]

i m gettin 1/2...

i m a bit confused as to how ratio of area to area has "pie" in the answer...

[sibbineni]

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

[raunekk]

@sibbineni

thx..i found my mistake!!

[missionmba]

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