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?
+128408 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
