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02 Feb 2022, 04:15
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D
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Difficulty:
25%
(medium)
Question Stats:
87% (02:10) correct
13%
(02:32)
wrong
based on 31
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What is the area of the shaded portion in circle O, as pictured above, with ∠O = 60° and radius r = 10?
A) \(\frac{50}{3}\pi-50\sqrt{3}\)
B) \(\frac{50}{3} \pi − 50\)
C) \(\pi \sqrt{3}\)
D) \(\frac{50}{3} \pi-25\sqrt{3}\)
E) \(\frac{50}{3} \pi\)
Attachment:
Geometry_Q14Image.jpg [ 6.99 KiB | Viewed 1088 times ]
kungfury42
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02 Feb 2022, 18:21
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Area of the sector = πr² / 6 = π(100/6) = 50π/3
Area of the equilateral triangle = (√3/4)*s² = (√3/4)*100 = 25√3
Subtracting the two, we get area of the shaded region = 50π/3 - 25√3
Hence, option D.
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Area of the equilateral triangle = (√3/4)*s² = (√3/4)*100 = 25√3
Subtracting the two, we get area of the shaded region = 50π/3 - 25√3
Hence, option D.
Posted from my mobile device
