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10 Jan 2019, 02:59
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E
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Difficulty:
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87% (01:21) correct
13%
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wrong
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In the circle above, three right angles have vertices at the center of the circle. If the radius of the circle is 8, what is the combined area of the shaded regions?
A. 8π
B. 9π
C. 12π
D. 13π
E. 16π
Attachment:
2019-01-10_1358.png [ 22.17 KiB | Viewed 5455 times ]
10 Jan 2019, 06:07
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In the circle above, three right angles have vertices at the center of the circle. If the radius of the circle is 8, what is the combined area of the shaded regions?
total 360 degrees are included in the circle, and in the figure non-shaded region is \(3*90 = 270 degrees\)
Area of the shaded region = 90 degrees
Area of the sector = \((x/360)*Pi*r^2\)
= \((90/360)*Pi*8*8\) --- radius given as 8
= \(16*PI\)
Option E is correct
total 360 degrees are included in the circle, and in the figure non-shaded region is \(3*90 = 270 degrees\)
Area of the shaded region = 90 degrees
Area of the sector = \((x/360)*Pi*r^2\)
= \((90/360)*Pi*8*8\) --- radius given as 8
= \(16*PI\)
Option E is correct
KanishkM
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10 Jan 2019, 06:27
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r = 8,
Area of shaded region will be 3 * \(\frac{theta}{360}\)* π \(r^2\) --------------------(1)
At the center of a circle, sum of the angles = \(360^o\)
Sum of remaining angles will be 360 - 270 = 90
So each shaded region will have an angle as\(\frac{90}{3}\)
Substituting this value in (1)
=\(\frac{3}{3}\)* \(\frac{90}{360}\)* π \(8^2\)
=16π
Answer E
Area of shaded region will be 3 * \(\frac{theta}{360}\)* π \(r^2\) --------------------(1)
At the center of a circle, sum of the angles = \(360^o\)
Sum of remaining angles will be 360 - 270 = 90
So each shaded region will have an angle as\(\frac{90}{3}\)
Substituting this value in (1)
=\(\frac{3}{3}\)* \(\frac{90}{360}\)* π \(8^2\)
=16π
Answer E
