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geometry

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You start with a circle of radius 1, and cut out a sector of angle 90 degrees.  The remaining 270 degree sector is rolled into a cone.  What is the height of the cone?

May 13, 2020

#1
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The circumference  of  the cone will be  (3/4) * 2 pi  r  =(6/4) pi* 1  =  (6/4) pi  = (3/2) pi

We can find  the radius  if the  cone as

(3/2)pi  =  2 pi * r     divide out pi

(3/2)  = 2 r       divide both sides by  2

(3/4) =  r

The orginal radius  will be  the slant height of the cone

And  the height of the cone  =  sqrt [  slant height^2  -  radius of cone ^2]  =

sqrt  [ 1^2  - (3/4)^2 ]  =

sqrt [ 1  - 9/16] =

sqrt [ 7/16] =

sqrt [7]   / 4

May 13, 2020
#2
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You start with a circle of radius 1 and cut out a sector of angle 90 degrees.  The remaining 270-degree sector is rolled into a cone.  What is the height of the cone?

2*pi = 6.283185307

[(6.283185307 / 4) *3] / pi = 1.5

The height of the cone      h = sqrt(1² - 0.75²)       h = 0.661437827

May 13, 2020