The side length of a square inscribed in a circle is 2. What is the ar : Problem Solving (PS)

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The side length of a square inscribed in a circle is 2. What is the ar

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The side length of a square inscribed in a circle is 2. What is the ar [#permalink]

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09 Oct 2018, 22:44

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73% (00:40) correct

27% (00:40) wrong

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The side length of a square inscribed in a circle is 2. What is the area of the circle?

(A) \(\pi\)

(B) \(\sqrt{2} \pi\)

(C) \(2\pi\)

(D) \(2 \sqrt{2} \pi\)

(E) \(\pi^2\)

Spoiler: OA

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Re: The side length of a square inscribed in a circle is 2. What is the ar [#permalink]

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09 Oct 2018, 22:54

Side of square inscribed in a circle is =2
Diagonal of square = diameter of circle = 2(2)^1/2

Radius of circle = (2)^1/2
Area of circle = pi(radius)^2
=2 x pi
Option :C

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The side length of a square inscribed in a circle is 2. What is the ar [#permalink]

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10 Oct 2018, 01:04

Bunuel wrote:

The side length of a square inscribed in a circle is 2. What is the area of the circle?

(A) \(\pi\)

(B) \(\sqrt{2} \pi\)

(C) \(2\pi\)

(D) \(2 \sqrt{2} \pi\)

(E) \(\pi^2\)

Area of the square = 2^2 = 4

Another way to find out area of the square = (1/2)*\(d^2\).

(1/2)\(d^2\) = 4

d = \(\sqrt{8}\)

Diameter =\(\sqrt{8}\)

Area of the circle = pie * \(r^2\)

= pie* \(((\sqrt{8})/2)^2\)
= 2 pie.

The best answer is C.