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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 be drawn into a wire of diameter , find the length of the wire.
In fig. cone ABC is cut out by a plane parallel to the base FG. DEFG is the frustum so obtained. Let O be the centre of the base of the cone and O’ the centre of the base of the frustum. It is given that ∠BAC = 60° ∠OAC = 30° In right triangle AOC, tan And, C = Height of the frustum = P'O = volume of the frustum =
Radius of the wire = Let h be length of the wire Volume of wire = From (iii) and (iv), we get |