• 2021 December(E23) Math Question 52

    Perimeter, Area, Volume

    - Triangles, Squares, Rectangles, Circles

    Arc Length, Perimeter of Circle
    Choice J
    52. A wire binds 4 identical posts together as shown below. Each post has a 3-inch radius. What is the length, to the nearest inch, of the shortest wire that will go around the 4 posts without overlap?

    Given that

    radius=r=3  inradius=r=3\; in
    =>circumference  of  a  circle=2πr=6π=>circumference\; of \; a \; circle=2\pi r=6\pi
    =>Length  of  an  arc={6π}{4}=> Length\; of\; an\; arc=\frac\{6\pi\}\{4\}
    =>Length  of  4  arcs={6π}{4}×4=6π=> Length\; of\; 4\; arcs=\frac\{6\pi\}\{4\}\times4=6\pi
    =>Length  of  4  blue  segments=6×4=24=> Length\; of\; 4\; blue\; segments=6 \times 4 =24
    ∴Length=6π+24=6(3.14)+24=42.84≈43\therefore Length=6\pi +24=6(3.14)+24=42.84\approx 43

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