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Circle Problem

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phoenix9801 Really wants to Beat The GMAT! Default Avatar
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Circle Problem Post Sun Jun 10, 2012 2:09 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    1-
    A large circular pizza with an area of 289π inches is placed inside a square box that is just large enough to hold it. If the box is two inches deep, what is the volume of the box in cubic inches?

    2-




    3-
    The circumference of a circle with an area of 225π is divided into 60 identical arcs. What is the length of each arc, divided by π ?

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    neelgandham Community Manager
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    Post Sun Jun 10, 2012 2:29 pm
    1-
    A large circular pizza with an area of 289π inches is placed inside a square box that is just large enough to hold it. If the box is two inches deep, what is the volume of the box in cubic inches?

    From the diagram:

    Let radius of the pizza be r. So, side of the square box = 2r
    We already know that the area of the pizza is 289*pi = pi*r*r
    So, r^2 = 289. So r = 17

    Volume of the box = Length of the box * Breath of the box * Height of the box
    Length of the box = 2r = 2*17 = 34 inches
    Breadth of the box = 2r = 2*17 = 34 inches
    Height of the box = 2 inches
    Volume of the box = 34*34*2 = 2312 cubic inches
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    neelgandham Community Manager
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    Post Sun Jun 10, 2012 2:32 pm
    The circumference of a circle with an area of 225π is divided into 60 identical arcs. What is the length of each arc, divided by π ?

    The area of a circle with radius r = π*r*r = 225*π. So, radius^2 = 225 and radius (r) = 15
    Circumference of the same circle = 2*π*r = 2*π*15 = 30*π
    If the circumference of the circle is divided into 60 identical arcs then length of each arc = 30*π/60 = π/2
    length of each arc, divided by π = (π/2)/π = 1/2

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    neelgandham Community Manager
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    Post Sun Jun 10, 2012 2:38 pm
    The area of a circle with radius r = π*r*r = 81*π. So, radius^2 = 81 and radius (r) = 9
    Circumference of the same circle = 2*π*r = 2*π*9 = 18*π.

    Since triangle DEF is an equilateral triangle. Length of arc DE = Length of arc EF = Length of arc FD
    Length of arc DE + Length of arc EF + Length of arc FD = Circumference of the circle
    3*Length of arc DE = Circumference of the circle
    3*Length of arc DE = 18*π
    Length of arc DE = 6*π
    Length of arc DE, divided by π = (6*π)/π = 6

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