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# If (#x) represents the area of a semicircle with diameter x, then (#2)

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Joined: 02 Sep 2009
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If (#x) represents the area of a semicircle with diameter x, then (#2)  [#permalink]

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14 Nov 2017, 01:23
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Difficulty:

45% (medium)

Question Stats:

65% (02:03) correct 35% (02:19) wrong based on 30 sessions

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If (#x) represents the area of a semicircle with diameter x, then (#2) + (#4) =

A. (#3)
B. (#5)
C. $$(#3 \sqrt{2})$$
D. $$(#2 \sqrt{5})$$
E. (#6)

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If (#x) represents the area of a semicircle with diameter x, then (#2)  [#permalink]

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14 Nov 2017, 02:22
1
1
(#x) represents the area of a semicircle with diameter x.

Formula:
Area of a semicircle = $$\frac{1}{2}$$*pi*r^2 where r-radius or diameter/2

(#2) = $$\frac{1}{2}*pi*1^2$$
(#4) = $$\frac{1}{2}*pi*2^2$$

(#2) + (#4) = $$\frac{1}{2}*pi*(1+4)$$ = $$\frac{1}{2}*pi*{5}$$

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*{2\sqrt{5}}^2*\frac{1}{2^2}$$ = $$\frac{1}{8}*pi*{4*5}$$ = $$\frac{1}{2}*pi*{5}$$

Therefore, (#2) + (#4) = $$(#2 \sqrt{5})$$(Option D)
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Re: If (#x) represents the area of a semicircle with diameter x, then (#2)  [#permalink]

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14 Nov 2017, 03:29
pushpitkc wrote:
(#x) represents the area of a semicircle with diameter x.

Formula:
Area of a semicircle = $$\frac{1}{2}$$*pi*r^2 where r-radius or diameter/2

(#2) = $$\frac{1}{2}*pi*1^2$$
(#4) = $$\frac{1}{2}*pi*2^2$$

(#2) + (#4) = $$\frac{1}{2}*pi*(1+4)$$ = $$\frac{1}{2}*pi*{5}$$

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*{2\sqrt{5}}^2*\frac{1}{2^2}$$ = $$\frac{1}{8}*pi*{4*5}$$ = $$\frac{1}{2}*pi*{5}$$

Therefore, (#2) + (#4) = $$(#2 \sqrt{5})$$(Option D)

Hi, kindly explain why (2\sqrt{5})^2 expression been multiplied by 1/2^2 in the 2nd last line.
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If (#x) represents the area of a semicircle with diameter x, then (#2)  [#permalink]

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14 Nov 2017, 05:11
pulkitarya wrote:
pushpitkc wrote:
(#x) represents the area of a semicircle with diameter x.

Formula:
Area of a semicircle = $$\frac{1}{2}$$*pi*r^2 where r-radius or diameter/2

(#2) = $$\frac{1}{2}*pi*1^2$$
(#4) = $$\frac{1}{2}*pi*2^2$$

(#2) + (#4) = $$\frac{1}{2}*pi*(1+4)$$ = $$\frac{1}{2}*pi*{5}$$

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*{2\sqrt{5}}^2*\frac{1}{2^2}$$ = $$\frac{1}{8}*pi*{4*5}$$ = $$\frac{1}{2}*pi*{5}$$

Therefore, (#2) + (#4) = $$(#2 \sqrt{5})$$(Option D)

Hi, kindly explain why (2\sqrt{5})^2 expression been multiplied by 1/2^2 in the 2nd last line.

Hi pulkitarya

The reason I have written it like that is for better readability. It should have been

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*(2\sqrt{5}/2)^2$$ = $$\frac{1}{2}*pi*{5}$$

Hope that helps!
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Joined: 16 Aug 2016
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Re: If (#x) represents the area of a semicircle with diameter x, then (#2)  [#permalink]

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14 Nov 2017, 05:30
pushpitkc wrote:
pulkitarya wrote:
pushpitkc wrote:
(#x) represents the area of a semicircle with diameter x.

Formula:
Area of a semicircle = $$\frac{1}{2}$$*pi*r^2 where r-radius or diameter/2

(#2) = $$\frac{1}{2}*pi*1^2$$
(#4) = $$\frac{1}{2}*pi*2^2$$

(#2) + (#4) = $$\frac{1}{2}*pi*(1+4)$$ = $$\frac{1}{2}*pi*{5}$$

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*{2\sqrt{5}}^2*\frac{1}{2^2}$$ = $$\frac{1}{8}*pi*{4*5}$$ = $$\frac{1}{2}*pi*{5}$$

Therefore, (#2) + (#4) = $$(#2 \sqrt{5})$$(Option D)

Hi, kindly explain why (2\sqrt{5})^2 expression been multiplied by 1/2^2 in the 2nd last line.

Hi pulkitarya

The reason I have written it like that is for better readability. It should have been

$$(#2 \sqrt{5})$$ = $$\frac{1}{2}*pi*(2\sqrt{5}/2)^2$$ = $$\frac{1}{2}*pi*{5}$$

Hope that helps!

thanks pushpitkc
Re: If (#x) represents the area of a semicircle with diameter x, then (#2) &nbs [#permalink] 14 Nov 2017, 05:30
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