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# In the figure shown, the circle has a diameter of 10, which

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In the figure shown, the circle has a diameter of 10, which [#permalink]

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Updated on: 12 Jun 2013, 02:32
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73% (01:40) correct 27% (01:38) wrong based on 109 sessions

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In the figure shown, the circle has a diameter of 10, which is also the side length of the implied square. If an outline is formed by half the circle, one quarter of the square, and a straight line connecting the perpendicular bisectors of the circle, what is the perimeter of this shape?

A. $$5+5(\pi + \sqrt{2})$$
B. $$10 + 10\pi +5 \sqrt{2}$$
C. $$10 + 5(\pi + \sqrt{2})$$
D. $$15 +\pi \sqrt{2}$$
E. $$10\pi\sqrt{3}$$

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Originally posted by fozzzy on 12 Jun 2013, 02:24.
Last edited by Bunuel on 12 Jun 2013, 02:32, edited 1 time in total.
Edited the stem and the answer choices.
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Posts: 46307
Re: In the figure shown, the circle has a diameter of 10, which [#permalink]

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12 Jun 2013, 02:37
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In the figure shown, the circle has a diameter of 10, which is also the side length of the implied square. If an outline is formed by half the circle, one quarter of the square, and a straight line connecting the perpendicular bisectors of the circle, what is the perimeter of this shape?

A. $$5+5(\pi + \sqrt{2})$$
B. $$10 + 10\pi +5 \sqrt{2}$$
C. $$10 + 5(\pi + \sqrt{2})$$
D. $$15 +\pi \sqrt{2}$$
E. $$10\pi\sqrt{3}$$

Diameter = 10 --> radius =5.

The perimeter of half the circle = $$\frac{2\pi{r}}{2}=5\pi$$;
The perimeter of half the square = $$r+r=10$$;
The length of the straight line = $$\sqrt{5^2+5^2}=5\sqrt{2}$$.

Total = $$5\pi+10+5\sqrt{2}$$.

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Re: In the figure shown, the circle has a diameter of 10, which [#permalink]

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12 Jun 2013, 02:39
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Given $$radius = 5$$, the circumference is $$2*5*\pi$$, so half circumference is $$5\pi$$.

Then we have two sides of a 5-side square, $$5+5=10$$

Then we have an hypostnus of a right triangle with two 5 sides, $$\sqrt{5^2+5^2}=2\sqrt{5}$$

Tot sum=$$5\pi+10+5\sqrt{2}$$
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Re: In the figure shown, the circle has a diameter of 10, which [#permalink]

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17 Apr 2017, 17:58
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Re: In the figure shown, the circle has a diameter of 10, which   [#permalink] 17 Apr 2017, 17:58
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