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OG2015 PS The figure above shows

This topic has 2 expert replies and 1 member reply
lionsshare Senior | Next Rank: 100 Posts
Joined
09 Aug 2017
Posted:
62 messages

OG2015 PS The figure above shows

Post Wed Sep 13, 2017 8:10 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])


    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) 25π
    (B) 38π
    (C) 55π
    (D) 57π
    (E) 64π

    OA: D

    Can anyone, please share the solution to this problem.

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    yasirnasir Junior | Next Rank: 30 Posts
    Joined
    07 Jun 2017
    Posted:
    11 messages
    Post Wed Sep 13, 2017 8:56 pm
    I think it is 57π 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 121π . Now, if we calculate the area of the circle only then it be 65π . By subtracting the circle area from total area, we will have the area of the path i.e. 121π - 65π = 57π .

    Post Wed Sep 13, 2017 9:28 pm
    lionsshare wrote:


    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) 25π
    (B) 38π
    (C) 55π
    (D) 57π
    (E) 64π

    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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    Post Tue Sep 19, 2017 3:02 pm
    lionsshare wrote:


    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) 25π
    (B) 38π
    (C) 55π
    (D) 57π
    (E) 64π

    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:

    π(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 = 57π

    Answer: D

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