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

Question

A metallic right circular cone 20 cm high and whose vertical angle is 60&#xB0; 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

Philoid · Accepted Answer

The figure is given below:

In ΔAEG,

⇒ EG = tan 30⁰ × AG

⇒ EG = (1/√3)× 10 cm

⇒ EG =

In ΔABD,

= tan 30^o

⇒ BD = tan 30⁰ × AD

⇒ BD =(1/√3)× 20 cm

⇒ BD =

Radius (r₁) = cm

Radius (r₂) = cm

Height (h) = 10 cm

Volume of frustum = (1/3)πh (r₁² + r₂² + r₁r₂)

= * π * 10 [()² + ()² + ]

= [ + + ]

= * *

= cm³

Radius (r) of wire = * = cm

Let the length of wire be l.

Volume of wire = Area of cross-section × Length

= (πr²) (l)

= π * ()² * l

Volume of frustum = Volume of wire

= * ()² * l

* 1024 = l

l = 796444.44 cm

= 7964.44 meters