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The diameter of circle S is equal in length to a side of a certain squ

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Bunuel
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The diameter of circle S is equal in length to a side of a certain squ [#permalink] New post   14 Oct 2019, 07:20
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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 a diagonal of the same square. The area of circle T is how many times the area of circle S ?


A. \(√2\)

B. \(√2 + 1\)

C. 2

D. \(\pi\)

E. \(\sqrt{2\pi}\)
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C
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Re: The diameter of circle S is equal in length to a side of a certain squ [#permalink] New post   14 Oct 2019, 07:26
Bunuel 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 a diagonal of the same square. The area of circle T is how many times the area of circle S ?


A. \(√2\)

B. \(√2 + 1\)

C. 2

D. \(\pi\)

E. \(\sqrt{2\pi}\)


Let the side of square = a & the radius of circle S & T are s & t respectively

The diameter of circle S is equal in length to a side of a certain square
--> 2s = a
--> s = a/2

The diameter of circle T is equal in length to a diagonal of the same square
--> 2t = √2a
--> t = a/√2

The area of circle T is how many times the area of circle S
--> \(\pi\)*t^2 = x*\(\pi\)*s^2
--> a^2/2 = x*a^2/4
--> x = 2

IMO Option C
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Re: The diameter of circle S is equal in length to a side of a certain squ [#permalink] New post   22 Oct 2019, 15:20
Bunuel 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 a diagonal of the same square. The area of circle T is how many times the area of circle S ?

A. \(√2\)

B. \(√2 + 1\)

C. 2

D. \(\pi\)

E. \(\sqrt{2\pi}\)


Since any two circles are similar, the ratio of their areas must be equal to the square of the ratio of their diameters.

\(A_T/A_S=(d_T/d_S)^2=(\sqrt{2}/1)^2=2\)

Answer: C
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Re: The diameter of circle S is equal in length to a side of a certain squ [#permalink] New post   24 Nov 2020, 11:13
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Bunuel 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 a diagonal of the same square. The area of circle T is how many times the area of circle S ?


A. \(√2\)

B. \(√2 + 1\)

C. 2

D. \(\pi\)

E. \(\sqrt{2\pi}\)


Let's solve the question by assigning some "nice" (easy to work with) values to the dimensions

Let's say each side of the square has length 2
This means 2 = the DIAMATER of circle S



If 2 = length of each side of square X, then the diagonal has length 2√2

This means 2√2 = the DIAMATER of circle T


The area of circle T is how many times the area of circle S ?
If 2 = the DIAMATER of circle S, then its RADIUS = 1
Area = πr² = π(1²) = π

If 2√2 = the DIAMATER of circle T, then its RADIUS = √2
Area = πr² = π(√2)² = 2π

The area of circle T is 2 times the area of circle S

Answer: C

Cheers,
Brent
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Re: The diameter of circle S is equal in length to a side of a certain squ [#permalink] New post   26 Mar 2023, 05:52
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Re: The diameter of circle S is equal in length to a side of a certain squ [#permalink]
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