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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

 Dec 22, 2023
 #1
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Surface area =

 

pi  [ L (R + r)   ]  +   pi ( R^2 + r^2 )             where  L = sqrt [H^2 + (R - r)^2 ]

 

So

 

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

 

pi [ sqrt ( 16 + 9)  *  (21)  ]  +  pi ( 225) =

 

pi [ 5 * 21 + 225 ] =

 

330 pi

 

Volume  =

 

pi  (H /  3 )   *   ( R^2  + Rr + r^2)

 

So

 

pi (4/3) * (12^2 + 12*9 + 9^2)   =

 

pi (4/3) * ( 144 + 108 + 81)  =

 

pi (4/3) ( 333) = 

 

444 pi

 

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

 

 

cool cool cool

 Dec 22, 2023

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