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The truncated right circular cone below has a large base radius $8$ cm and a small base radius of $4$ cm. The height of the truncated cone is $10$ cm.  The volume of this solid is $n \pi$ cubic cm, where $n$ is an integer.  What is $n$?

 Aug 30, 2023
 #1
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This solid  is known  as a frustum.....

 

Volume of frustum, V = H3(S1+S2+√S1S2), where

H = Height of the frustum (the distance between the centers of two bases of the frustum)

S1 = Area of one base of the frustum

S2 = Area of the other base of the frustum

 

Area of  large base =  pi *(8)^2 =  64 pi

Area of small base = pi* (4)^2 =   16pi

 

Volume =    (1/3) (10cm)  ( 64 pi + 16 pi  +  sqrt ( 64 pi * 4 pi) )  =

 

(10/3) (64 pi + 16pi  +  sqrt (256 pi^2) )  =

 

(10/3) ( 64 pi + 16 pi + 16 pi)  =

 

10 ( 96 pi)  /  3 =  

 

320  pi   cm^2

 

n = 320

 

cool cool cool

 Aug 30, 2023

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