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In the figure above, arcs PR and QS are semicircles with centers at Q

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In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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28 Nov 2017, 20:19
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25% (medium)

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82% (01:17) correct 18% (02:14) wrong based on 51 sessions

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In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

Attachment:

2017-11-29_0807.png [ 32.32 KiB | Viewed 1122 times ]

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Re: In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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28 Nov 2017, 21:42
The radius of both the circles is equal and is 5 . Hence, the total perimeter is equal to 2πR+2R.
Hence the perimeter is equal to 10πr+10.
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In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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30 Nov 2017, 15:21
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Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

Attachment:
2017-11-29_0807.png

Because semicircle PR is centered at Q, its radius = QR = PQ (given) = 5. Because semicircle QS is centered at R, its radius, too, is QR = 5.

Perimeter:

Segment PQ = 5
Segment RS = 5

Arc PR = $$\frac{2πr}{2}=\frac{10π}{2}= 5π$$

Arc QS = $$\frac{2πr}{2}=\frac{10π}{2}= 5π$$

Total: 10 + 10π

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Re: In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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30 Nov 2017, 19:17
Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

Attachment:
2017-11-29_0807.png

we have r = 5 for each circle
perimeter of half circle = Pi * r

so perimeter of the shaded region = perimeter of both half circles + r1 + r2 = 2*5*pi + 5 + 5 = 10pi + 10
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Re: In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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01 Dec 2017, 06:53
Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

Attachment:
2017-11-29_0807.png

We see that the radii of both semicircles is 5.

Thus, the semicircular arc of each semicircle (half circumference) is 1/2 x 2π(5) = 5π. We also see that PQ = RS = 5. Thus the perimeter of the shaded region is:

5π + 5π + 5 + 5 = 10π + 10

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Re: In the figure above, arcs PR and QS are semicircles with centers at Q  [#permalink]

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20 Mar 2018, 10:52
Hi All,

There's a great "pattern" behind this question.

Since we're dealing with 2 semi-circles, and QR represents the SAME radius in both of them, we know that the 2 semi-circles are IDENTICAL. Thus, the perimeter of the shape is made up of….

The circumference of one full circle + the diameter of that circle.

Since the radius = 5, we know….
Circumference = 2r(pi) = 10pi
Diameter = 2r = 10
Total perimeter = 10pi + 10

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Re: In the figure above, arcs PR and QS are semicircles with centers at Q   [#permalink] 20 Mar 2018, 10:52
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