GMAT PREP PS question

[alex.gellatly]

A square is inscribed in a circle. If the area of the square region is 16, what is the area of the circular region?

(A) 2pi
(B) 4pi
(C) 6pi
(D) 12pi
(E) 16pi

Thanks

[Anurag@Gurome]

A square is inscribed in a circle. If the area of the square region is 16, what is the area of the circular region?

(A) 2pi
(B) 4pi
(C) 6pi
(D) 12pi
(E) 16pi

Thanks

Area of the square region is 16.
If each side of the square = s, then area of square = s²
s² 16 implies s = 4
Now we can find length of diagonal AC, which is the diameter of the circle.
By Pythagoras Theorem, AC² = AB² + BC²
AC² = 4² + 4² = 32
AC = √32 = 4√2

This means radius of circle = 2√2
Area of circle = (pi) * radius² = (pi) * (2√2)² = [spoiler]8(pi) [/spoiler]sq units, which is not given in the answer choices.

[aneesh.kg]

If the area of the square is 16, then each side of the square must be 4.

Please note that, the diameter of the circle which is also the diagonal of a square.

Using Pythagoras' Theorem to find the length of the diagonal of the square,

d^2 = 4^2 + 4^2
or
d = 4 . (2)^0.5
or
r = 2 . (2)^0.5

Area of the circle = pi.(r)^2
= pi . 8

The answer is 8pi (which is surprisingly not in the options)