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# If the perimeter of a semi-circle is 4π + 8, what is the area of the s

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
If the perimeter of a semi-circle is 4π + 8, what is the area of the s  [#permalink]

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09 Sep 2018, 07:55
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Difficulty:

45% (medium)

Question Stats:

68% (01:37) correct 32% (02:28) wrong based on 27 sessions

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If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?

A. 16π
B. 8π
C. 4π
D. 8
E. 4

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Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
If the perimeter of a semi-circle is 4π + 8, what is the area of the s  [#permalink]

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09 Sep 2018, 08:13
Bunuel wrote:
If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?

A. 16π
B. 8π
C. 4π
D. 8
E. 4

perimeter of a semi circle = $$\pi$$r + 2r
so,
$$\pi$$r + 2r = 4$$\pi$$ + 8
r($$\pi$$+2)= 4($$\pi$$ + 2)
r=4
area = $$\pi$$$$r^2$$/2 = 8$$\pi$$
CEO
Joined: 11 Sep 2015
Posts: 3429
Re: If the perimeter of a semi-circle is 4π + 8, what is the area of the s  [#permalink]

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09 Sep 2018, 08:28
Top Contributor
Bunuel wrote:
If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?

A. 16π
B. 8π
C. 4π
D. 8
E. 4

Let r = the RADIUS of the circle
So, the length of the diameter = 2r

The circumference of an ENTIRE circle = 2πr
So, the circumference of a SEMIcircle = 2πr/2 = πr

We get:

So the PERIMETER = πr + 2r
We're told that the PERIMETER = 4π + 8

We can write: πr + 2r = + 8
We can see that, if r = 4, the equation holds true
So, the radius must be 4

What is the area of the semi-circle?
Area of circle = πr²
So, area of SEMIcircle = πr²/2
So, the area of the given circle = π(4²)/2
= 16π/2
= 8π

Cheers,
Brent
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Re: If the perimeter of a semi-circle is 4π + 8, what is the area of the s   [#permalink] 09 Sep 2018, 08:28
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