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 (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)
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