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by lionsshare » Wed Sep 13, 2017 8:10 pm
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The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) 25Ï€
(B) 38Ï€
(C) 55Ï€
(D) 57Ï€
(E) 64Ï€

OA: D

Can anyone, please share the solution to this problem.
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by yasirnasir » Wed Sep 13, 2017 8:56 pm
I think it is 57Ï€ or option D.

If the circle and the path are taken together then the radius becomes 8 feet plus 3 feet = 11 feet

Formula to calculate the area of circles is: π r^2
By calculating the total area, it will be 121Ï€ . Now, if we calculate the area of the circle only then it be 65Ï€ . By subtracting the circle area from total area, we will have the area of the path i.e. 121Ï€ - 65Ï€ = 57Ï€ .
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by Jay@ManhattanReview » Wed Sep 13, 2017 9:28 pm
lionsshare wrote:Image

The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) 25Ï€
(B) 38Ï€
(C) 55Ï€
(D) 57Ï€
(E) 64Ï€

OA: D

Can anyone, please share the solution to this problem.
The radius of the outer edge of the path = 8 + width of the flower bed (= 3)

The radius of the outer edge of the path = 8 + 3 = 11 feet

Area of the path = Area of the outer circle of the path - Area of the inner circle of the path = π .(11)^2 - π .(8)^2 = 121π - 64π = 57π sq feet

The correct answer: D

Hope this helps!

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by Jeff@TargetTestPrep » Tue Sep 19, 2017 3:02 pm
lionsshare wrote:Image

The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?

(A) 25Ï€
(B) 38Ï€
(C) 55Ï€
(D) 57Ï€
(E) 64Ï€

OA: D
The circular path (i.e., the shaded region) is called an annulus in geometry. Basically an annulus is a ring-shaped figure bounded by two concentric circles. To find the area of an annulus, we use the following formula:

Ï€(R^2 - r^2)

where r is the radius of the inner circle and R is the radius of the outer circle.

We know:

R = 8 + 3 = 11 feet

r = 8 feet

Plugging into our equation, we have:

area = π(11^2 - 8^2)

area = π(121 - 64)

area = 57Ï€

Answer: D

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