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07 Oct 2021, 04:15
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In the figure above, the centers of all three circles lie on the same line. The radius of the middle-sized circle is twice that of the smallest circle. If the radius of the smallest circle is 1, what is the length of the boundary of the shaded region?
(A) 9
(B) \(3π\)
(C) 12
(D) \(6π\)
(E) \(12π\)
Attachment:
1.jpg [ 10.68 KiB | Viewed 3026 times ]
07 Oct 2021, 04:29
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Boundary of the shaded region will be the sum of half the circumference of each circle.
Circumference of circle: \(πd\)
Biggest circle: \(6π\) half= \(3π\)
Middle circle: \(4π\) half= \(2π\)
Smallest circle: \(2d\) half= \(π\)
\(3π + 2π + π = 6π \)
Answer D
Circumference of circle: \(πd\)
Biggest circle: \(6π\) half= \(3π\)
Middle circle: \(4π\) half= \(2π\)
Smallest circle: \(2d\) half= \(π\)
\(3π + 2π + π = 6π \)
Answer D
The smallest circle has a radius of 1
the middle-sized circle has a radius of 2
the diameter of the large circle must be 6, which makes its radius 3.
The arc of a semicircle is half the circle’s circumference – πr.
The length of the boundary of the shaded region is the sum of the arcs of the three semicircles: π + 2π + 3π = 6π.
Option D
the middle-sized circle has a radius of 2
the diameter of the large circle must be 6, which makes its radius 3.
The arc of a semicircle is half the circle’s circumference – πr.
The length of the boundary of the shaded region is the sum of the arcs of the three semicircles: π + 2π + 3π = 6π.
Option D
