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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# 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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The diagram will be as follows

Consider AEG

Radius (r

_{1}) of upper end of frustum = (10√3)/3 cmRadius (r

_{2}) of lower end of container = (20√3)/3 cmHeight (r

_{3}) of container = 10 cmNow,

Volume of the frustum = (⅓)×π×h(r

_{1}^{2}+r_{2}^{2}+r_{1}r_{2})Solving this we get,

Volume of the frustum = 22000/9 cm

^{3}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

= (πr

^{2})xl= π(1/32)

^{2}x lNow, Volume of frustum = Volume of wire

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

^{2}x lSolving this we get,

l = 7964.44 m