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 cm, find the length of the wire.

Answer 1

In ΔAEG,

In ΔABD,

Radius (r₁) of upper end of frustum = cm

Radius (r₂) of lower end of container =

Height (h) of container = 10 cm

Volume of frustum

Radius (r) of wire =

Let the length of wire be l.

Volume of wire = Area of cross-section × Length

= (πr²) (l)

Volume of frustum = Volume of wire