- 400 The key to solving this question is to recognize that the diameter of the
circle is the diagonal of the square:
To solve for the area of the square, first solve for the diagonal: if area of the
circle = 200π, then
200π = π(r^2 )
200 = r^2
10√ 2 = r
If r = 10√ 2 , then the diameter = 20√ 2. The diagonal of the square is thus 20√ 2.
Recall that the diagonal of a square forms two 45-45-90 triangles. The side
length of the square will be the leg of one of the 45-45-90 triangles. Since the
hypotenuse of one of the resulting 45-45-90 triangles is 20√ 2 , the length of
the leg will be 20. Thus the side of the square = 20. The area of the square is
202 = 400.- D The area of the shaded region = area of the larger circle – area of the pond.
You are told that the area of the pond is 81π, so solve for the area of the larger
circle. The radius of the larger circle = the radius of the pond + width of the
garden. Use the area formula to solve for the radius of the pond:
81π = πr^2
81 = r^2
9 = r
Add 9 to the width of the garden: 9 + 2 = 11. The radius of the larger circle is
thus 11, and its area is π(11^2 ) = 121π. The area of the shaded region is thus:
121π – 81π = 40π. - B Since the central angle measures 120, the sector area =^120360 × the circle
area =^120360 × π3^2 =^13 (9π) = 3π.
CHAPTER 13 ■ GEOMETRY 41904-GRE-Test-2018_313-462.indd 419 12/05/17 12:05 pm