Unformatted text preview: ﬁgure 9.22 . The angle at the center, in radians, is then 2 πr/h , and the area of the cone is equal to the area of the sector of the circle. Let A be the area of the sector; since the area of the entire circle is πh 2 , we have A πh 2 = 2 πr/h 2 π A = πrh. Now suppose we have a frustum of a cone with slant height h and radii r and r 1 , as in ﬁgure 9.23 . The area of the entire cone is πr 1 ( h + h ), and the area of the small cone is πr h ; thus, the area of the frustum is πr 1 ( h + h )πr h = π (( r 1r ) h + r 1 h ). By similar triangles, h r = h + h r 1 ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Approximation, Cone

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