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

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

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New post 23 Aug 2018, 02:27
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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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Re: A ten-foot high fence is being erected around a circular park with an  [#permalink]

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New post 23 Aug 2018, 03:33
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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Re: A ten-foot high fence is being erected around a circular park with an  [#permalink]

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New post 27 Aug 2018, 01:47
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)
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Re: A ten-foot high fence is being erected around a circular park with an &nbs [#permalink] 27 Aug 2018, 01:47
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