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A frustum of a right circular cone is formed by cutting a small cone off of the top of a larger cone. If a particular frustum has an altitude of 24 centimeters, the area of its lower base is 100\pi sq cm and the area of its upper base is 25\pi sq cm, what is the altitude of the small cone that was cut off?

 Dec 1, 2020
 #1
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Find the radius  of the  lower base

 

100/pi   =  pi ^ r^2

100/pi^2  = r^2             take the root of both sides

10/pi   = r

 

Find the  radius of the upper base

 

25/pi =  pi * r^2

25/pi^2   = r^2     take the root of both sides

5/pi  =  r

 

Using similar triangles, call  H  the height that was cut off

 

H/ [H + 24]  =  [ 5/pi ] / [10/pi ]

 

H / [ H + 24 ]  = 5/10

 

H / [ H +24 ] =  1/2   cross-multiply

 

2H  = H + 24

 

2H - H  = 24

 

H =  24 cm

 

 

cool cool cool

 Dec 1, 2020

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