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.[Use π = 22/7]

Answer 1

In ΔAEG,

In ΔABD,

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

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

Height (h) of container = 10 cm

Volume of frustum

 

Radius (r) of wire = 1/16 x 1/2 = 1/32 cm

Let the length of wire be l.                                      

Volume of wire = Area of cross-section × Length = (πr²) (l)

= π (1/32)² x l

Volume of frustum = Volume of wire