BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Diameter of circle S... help!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 88
Joined: Sat Oct 15, 2011 6:38 pm
Thanked: 1 times
Followed by:1 members

Diameter of circle S... help!

by gmatpup » Tue Jan 24, 2012 8:44 am
The diameter of circle S is equal in length to a side of a certain square. The diameter of circle T is equal in length to the diagonal of the same square. The area of circle T is how many times the area of circle S?

A. squareroot 2
B. squareroot 2 +1
C. 2
D. pie
E. squareroot 2n

Anwswer is C


Please explain, thanks so much!!
Top
Source: — Problem Solving |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Tue Jan 24, 2012 9:31 am
the ratio between two diameters is sqrt(2) - rule 45`,45`,90` right triangle
radii will be different ine the same ratio of sqrt(2)
circle T has larger area than circle S, T(pi*r^2)/S(pi*r^2)=2
gmatpup wrote:The diameter of circle S is equal in length to a side of a certain square. The diameter of circle T is equal in length to the diagonal of the same square. The area of circle T is how many times the area of circle S?

A. squareroot 2
B. squareroot 2 +1
C. 2
D. pie
E. squareroot 2n

Anwswer is C


Please explain, thanks so much!!
Success doesn't come overnight!
Top
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Fri Aug 12, 2011 12:37 am
Thanked: 3 times
Followed by:1 members

by sk8legend408 » Tue Jan 24, 2012 11:08 am
Pick numbers. If the diameter for circle S is 4, the side of the square is also 4. The radius is 2 and the area is πr^2 = 4π.

Both sides of the square are 4 so the pythagorean theorem can be applied or as pemdas alluded to the 45, 45, 90 right triangle rule can be applied.

Pythagorean theorem - 4^2 + 4^2 = C^2. 16 + 16 = 32 = C^2. C = sqrt (32) = 4sqrt(2) = diameter of circle T. The radius for circle T is half of the diameter or 2sqrt(2). The area of circle T is (2sqrt(2))^2 * π = 4*2*π = 8π.

8Ï€ is two times 4Ï€.
Top
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Tue Jan 24, 2012 11:46 am
Diameter of S=a
Diameter of T=2^1/2a[diagonal of the square]

so Area of T is twice the area of S
Top
Post new topic Post Reply
• Page 1 of 1