Circles

SAT Math· difficulty 5/5

A square is inscribed in a circle of radius 5. What is the area of the region inside the circle but outside the square?

  • A

    25π5025\pi - 50

    check_circle
  • B

    25π2525\pi - 25

  • C

    25π10025\pi - 100

  • D

    10π5010\pi - 50

Explanation

Diagonal of square = diameter = 10. Side =frac10sqrt2=5sqrt2= \\frac{10}{\\sqrt{2}} = 5\\sqrt{2}. Square area =(5sqrt2)2=50= (5\\sqrt{2})^2 = 50. Circle area =25pi= 25\\pi. Difference =25pi50= 25\\pi - 50.

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