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A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire. Q.5

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Find the best solution of ncert class 10 chapter surface areas and volumes . Give me the best solution of the exercise 13.4 question no. 5 . Sir please give me the easiest and simplest  solution of this question. A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire.

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  1. The diagram will be as follows

    NCERT Solutions Class 10 chapter 13-27

    Consider AEG

    Ncert solutions class 10 chapter 13-29

    Radius (r1) of upper end of frustum = (10√3)/3 cm

    Radius (r2) of lower end of container = (20√3)/3 cm

    Height (r3) of container = 10 cm

    Now,

    Volume of the frustum = (⅓)×π×h(r12+r22+r1r2)

    Ncert solutions class 10 chapter 13-30

    Solving this we get,

    Volume of the frustum = 22000/9 cm3

    The radius (r) of wire = (1/16)×(½) = 1/32 cm

    Now,

    Let the length of wire be “l”.

    Volume of wire = Area of cross-section x Length

    = (πr2)xl

    = π(1/32)2x l

    Now, Volume of frustum = Volume of wire

    22000/9 = (22/7)x(1/32)2x l

    Solving this we get,

    l = 7964.44 m

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