circumf of circle

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g.shankaran: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Oct 27, 2009 8:19 amFollowed by: 2 members; Thanked: 4 times

by g.shankaran » Thu Jun 09, 2011 8:03 am

Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T

1. 6 pi
2. 12 pi
3. 3 sqr (2pi)
4. 6 sqr (2pi)
5. 12 sqr (2 pi)

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Source: Beat The GMAT — Problem Solving | Thu Jun 09, 2011 8:03 am

bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Thu Jun 09, 2011 8:08 am

[spoiler]6pi(sqrt)2[/spoiler]

Regards,

Pranay

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Thu Jun 09, 2011 8:08 am

let side of square=a
then 4a=24 -> a=6
diagonal = 6*root(2) = diameter of circle
thus circumference = diameter*pi
IMO D

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Thu Jun 09, 2011 11:47 am

Perimeter = 24, side = 24 /4 = 6

Area of square = 36

1/2 Diagonal^2 = 36

Diagonal= root 72 = 6 root 2

radius = 3 root 2

Circumference = 2 TTr = 2* 3 root 2 * TT = 6 TT root2

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jainnikhil02: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue May 31, 2011 12:26 amFollowed by: 1 member; Location: Hyderabad; Thanked: 5 times

by jainnikhil02 » Thu Jun 09, 2011 11:59 am

[spoiler]6pi(root3)[/spoiler]

Nikhil K Jain
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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Jun 09, 2011 12:02 pm

MBA.Aspirant wrote:Perimeter = 24, side = 24 /4 = 6

Area of square = 36

1/2 Diagonal^2 = 36

Diagonal= root 72 = 6 root 2

radius = 3 root 2

Circumference = 2 TTr = 2* 3 root 2 * TT = 6 TT root2

Great solution!

A lesser known formula for the area of a square is:

area = (diagonal^2)/2

which is derived from the Pythagorean theorem (using 45/45/90 ratios).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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