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# A ten-foot high fence is being erected around a circular park with an

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Math Expert
Joined: 02 Sep 2009
Posts: 49251
A ten-foot high fence is being erected around a circular park with an  [#permalink]

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23 Aug 2018, 03:27
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:48) correct 23% (00:44) wrong based on 31 sessions

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A ten-foot high fence is being erected around a circular park with an area of 25π square feet. How many square feet of fencing are required to complete the task?

A. $$250\pi$$

B. $$100\pi$$

C. $$50\pi$$

D. $$25\pi$$

E. $$5\pi$$

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Math Expert
Joined: 02 Aug 2009
Posts: 6785
Re: A ten-foot high fence is being erected around a circular park with an  [#permalink]

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23 Aug 2018, 04:33
Bunuel wrote:
A ten-foot high fence is being erected around a circular park with an area of 25π square feet. How many square feet of fencing are required to complete the task?

A. $$250\pi$$

B. $$100\pi$$

C. $$50\pi$$

D. $$25\pi$$

E. $$5\pi$$

Two ways to look at it..

1) as a cylinder
So we are looking at the curved surface as the top and bottom of this cylinder are not to be covered.
Area of base=25π=π*r^2.......r=5
Curved surface area =2πrh=2π*5*10=100π

2) after we have got perimeter as 2πr and height of h
Open this and you get a rectangle of sides 2πr and H..

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A ten-foot high fence is being erected around a circular park with an  [#permalink]

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27 Aug 2018, 02:47
One way to look at the problem is to regard the fencing as a bigger circle that extends the smaller one by a "width" of 10.
Thus, we should calculate the Area of the bigger circle - Area of the smaller circle.

From the stem we know that the radius of the smaller circle must be 5. Hence, the radius of the bigger circle is 5+10=15.
Now we can calculate the area of the bigger circle$$= 15^2*π$$.

The answer we are looking for is: 125π-25π = 100π (B)
Re: A ten-foot high fence is being erected around a circular park with an &nbs [#permalink] 27 Aug 2018, 02:47
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