SOLUTION: A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm. The remaining part is folded to form a cone. Find 1. the ver

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Question 1183412: A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm. The remaining part is folded to form a cone. Find 1. the vertical angle of the cone 2. The angle of the sector.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Length of arc = +%28%28theta%29%2F360%29%2A+%28pi%29%2Ad%29
length of arc p = 110/360 (2*pi*70)
p= 1540/36 * pi
area of major arc = (140 *pi -(1540/36)*(pi))
= 97.2 *pi
The area of major arc is the circumference of the base of cone
97.2*pi = d *pi
d= 97.2
r = 48.6
Now the radius of the circle becomes the slant height of the cone
height of cone h=+sqrt%28l%5E2-r%5E2%29
height of cone = sqrt%2870%5E2-48.6%5E2%29
height of cone = 50.37
we know radius and height angle of cone can be calculated