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The cone below has a lateral surface area of $16 \sqrt{5} \cdot \pi$.  Find the volume of the cone.

 

 Mar 12, 2024
 #1
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\(16 \sqrt{5} \cdot \pi \)

 

L =  10

 

16sqrt( 5)  pi =  pi * r * L

 

16sqrt 5  =  10 * r

 

r  =  (16sqrt 5) / (10)  =  (8sqrt 5) / ( 5) =  8 / (sqrt(5))

 

Volume of  cone =  (1/3) pi [ 8/ sqrt(5)  ]^2 * sqrt  [ 10^2  - [ 8 /sqrt (5)]^2 ]   ≈  125.17

 

cool cool cool

 Mar 12, 2024
edited by CPhill  Mar 12, 2024

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