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A cone has a base radius of 6, and a lateral surface area of 12sqrt34*pi. Find the volume of the cone.

 Feb 5, 2020
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Lateral  surface area  =  

 

pi  * radius * slant height of cone

 

So

 

12√34 * pi  = pi * 6 * slant height of cone    [ divide out pi ]

 

12√34 =  6 * slant height of cone    [divide both sides by 6 ]

 

2√34 =  slant height of  cone  =   √ [ 34 * 4 ]  =  √ 136

 

Using the  Pythagorean Theorem......the height of the cone  =

 

√[ (√136)^2  -6^2 ]  = √ [136 - 36 ] =  √100  =  10

 

So.....the volume of the cone is

 

(1/3) pi * radius^2 * height  =

 

(1/3) pi (6)^2 * 10  =

 

(1/3) pi * 360  =

 

120 pi     units^3

 

cool cool cool

 Feb 5, 2020
edited by CPhill  Feb 5, 2020

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