two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped,

[BTGmoderatorLU]

Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. \(1 : 2\)
B. \(\pi : 2\)
C. \(1 : 1\)
D. \(4 : \pi\)
E. The ratio depends on the length of the two strings

The OA is D

[gmatter2012]

Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. \(1 : 2\)
B. \(\pi : 2\)
C. \(1 : 1\)
D. \(4 : \pi\)
E. The ratio depends on the length of the two strings

The OA is D

ans should be \4 \pi :1 \ rather than 4 : \ pi

[gmatter2012]

Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. \(1 : 2\)
B. \(\pi : 2\)
C. \(1 : 1\)
D. \(4 : \pi\)
E. The ratio depends on the length of the two strings

The OA is D

ans should be \(4 \pi :1\) rather than \(4 : \pi \)

[regor60]

Source: GMAT Prep

Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?

A. \(1 : 2\)
B. \(\pi : 2\)
C. \(1 : 1\)
D. \(4 : \pi\)
E. The ratio depends on the length of the two strings

The OA is D

ans should be \(4 \pi :1\) rather than \(4 : \pi \)

L= length of strings

Circumference of circle=L=2piR
R=L/2pi.

Area of circle: piR^2= pi*L^2/4pi^2
= L^2/4pi

Each side of square= L/4

Area of square: L^2/16

Ratio of area of circle to area of square means:
Area of circle/Area of square

= (L^2/4pi)/(L^2/16)
= (L^2/4pi)*(16/L^2)
=4/pi which is 4:pi D