SOLUTION: A sector of angle 65° is removed to form a thin circular sheet of radius 15cm and folded to form a right circular cone. Calculate the volume of the cone
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Question 1206673: A sector of angle 65° is removed to form a thin circular sheet of radius 15cm and folded to form a right circular cone. Calculate the volume of the cone Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! A sector of angle 65° is removed to form a thin circular sheet of radius 15cm and folded to form a right circular cone. Calculate the volume of the cone
Volumeof cone = 1/3 * pi*r^2*h
we need to find h the height and radius of base of cone (r)
Area of sector = ((theta)/360 )* pi*r^2
A=(65/360)*pi*15^2
A= 127.627 cm^2
When folded the area of sector will be the lateral surface area of cone = pi*r*l.
radius of sector will become the slant height of cone
pi*r*15= 127.627
r=127.627/ (15*pi)
r=2.708 cm
h= sqrt(l^2-r^2)
h = sqrt(15^2-2.708)^2)= 14.75
Volume of cone = (1/3) *pi*(2.708)^2*14.75
= 113.27 cm^3
