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A conical frustum has bases with radii of 9 and 12 and a height of 4. The total surface area of the frustum is A, in square units, and the volume of the frustum is V, in cubic units. Find A + V.

 
 Aug 5, 2022
edited by Dachenster  Aug 5, 2022
 #1
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See https://web2.0calc.com/questions/tricky-3d-geo-prob

 
 Aug 5, 2022
 #2
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See https://web2.0calc.com/questions/please-help-cphill-asap

 
 Aug 5, 2022
 #3
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Volume = pi (h/3)(a^2 + ab + b^2)     where h is the  height and  a, b are the radii 

 

Surface area  = pi  [ (a + b) sqrt   [ ( a  -b)^2 + h^2 ]  + a^2 + b^2  ] 

 

Filling in what we know

 

pi [ (9 +12) sqrt [ (12 - 9 )^2 + 4^2 ] + 12^2 + 9^2  ]  = 330pi  = A

 

pi (4/3) (12^2 + 12*9 + 9^2  ]  =  444pi  =  V

 

A + V =     330pi + 444 pi  =   774 pi   

 

 

cool cool cool

 
 Aug 5, 2022

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