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A square is inscribed in a circle. If the area of the inscribed square is 50, what is the area of the circle?
A square is inscribed in a circle. If the area of the inscribed square is 50, what is the area of the circle?
admin
2013-05-19
2
问题
A square is inscribed in a circle. If the area of the inscribed square is 50, what is the area of the circle?
选项
A、5π
B、5π
C、10π
D、25π
E、50π
答案
D
解析
The correct answer is D. If the area of the square is 50, then one side of the square is
or
. The diagonal of an inscribed square is equal to the diameter of the circle. The diagonal creates 2 isosceles right triangles. Use the Pythagorean Theorem:
. Simplify the equation and you get c=10. If the diameter is 10, then the radius is 5. Since the area of a circle is πr
2
, the area of this circle is 25π.
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