+101 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
+129771 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
