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PQ is a diameter of the circle centered at O. If the area of sector RS
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04 Jan 2023, 09:25
04 Jan 2023, 09:25
Expert Reply
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71% (01:29) correct
28% (01:11) wrong based on 7 sessions
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PQ is a diameter of the circle centered at O. If the area of sector RSPO equals \(4 \pi\), then the circumference of the circle is how many times \(\pi\)?
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PQ is a diameter of the circle centered at O. If the area of sector RS
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10 Feb 2023, 15:05
10 Feb 2023, 15:05
Expert Reply
OE
Because angle ROQ is a right angle and POQ is a straight line, angle POR must also be a right angle. Angle POR is the central angle of sector RSPO. Therefore, the area of sector RSPO must be 1/4 of the entire circle (90° is one-fourth of 360°). The area of the entire circle is found as follows: 4 x 417= 16 tt. Using the area formula for a circle, you obtain \(\pi r^2=16 \pi \) or \(r=\sqrt{16}=4\)
Finally, the circumference of the circle is found from the formula \(c = 2 \pi r = 8 \pi.\) The circumference of the circle is 8 times \(\pi\)
Because angle ROQ is a right angle and POQ is a straight line, angle POR must also be a right angle. Angle POR is the central angle of sector RSPO. Therefore, the area of sector RSPO must be 1/4 of the entire circle (90° is one-fourth of 360°). The area of the entire circle is found as follows: 4 x 417= 16 tt. Using the area formula for a circle, you obtain \(\pi r^2=16 \pi \) or \(r=\sqrt{16}=4\)
Finally, the circumference of the circle is found from the formula \(c = 2 \pi r = 8 \pi.\) The circumference of the circle is 8 times \(\pi\)
gmatclubot
PQ is a diameter of the circle centered at O. If the area of sector RS [#permalink]
10 Feb 2023, 15:05
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