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avatar+1121 

A sphere of radius $4$ inches is inscribed in a cone with a base of radius $8$ inches.  In inches, what is the height of the cone?  Express your answer as a decimal to the nearest tenth.

 Mar 29, 2024
 #1
avatar+128794 
+1

          A

         

                       D

                 4

          E            8           C       

 

 triangle  ADE  similar to triangle  AEC

 

AE / DE  = AC / EC

 

h / 4  = sqrt [h^2 + 8^2] / 8  

 

8h  =  4sqrt [ h^2 + 64]

 

2h  = sqrt [ h^2 + 64 ]       square both sides

 

4h^2  = h^2  +  64

 

3h^2    =  64

 

h^2  =  64 / 3

 

h = 8 / sqrt 3  ≈   4.6

 

cool cool cool

 Mar 29, 2024

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