A solid 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 1⁄12 find the length of the wire.
A2440 m
B2560 m
C4480 m
D3280 m
Ans 1:
Class : Class 10
C. 4480 m
VOLUME OF FRUSTUM= VOLUME OF WIRE
(calculate radius using trigonometry)
R=radius of original cone, H=height of original cone, r=radius of new cone, h=height of new cone, r₁²=radius of wire, h₁=height/length of wire
vol. of frustum= vol. of original cone- vol. of smaller cone (cut off) => 1/3πR²H - 1/3πr²h => 1/3π*7000/3cm³
vol. of wire(cylinder) = πr₁²h₁ => π1/24*1/24*h
equating and cancelling on both sides of equation,
7000= h/64
h=448000cm = 4480 m
Ans 2:
Class : Class 10
C. 4480 m
VOLUME OF FRUSTUM= VOLUME OF WIRE
(calculate radius using trigonometry)
R=radius of original cone, H=height of original cone, r=radius of new cone, h=height of new cone, r₁²=radius of wire, h₁=height/length of wire
vol. of frustum= vol. of original cone- vol. of smaller cone (cut off) => 1/3πR²H - 1/3πr²h => 1/3π*7000/3cm³
vol. of wire(cylinder) = πr₁²h₁ => π1/24*1/24*h
equating and cancelling on both sides of equation,
7000= h/64
h=448000cm = 4480 m