solid mensuration

Let the lower base  = R   and  the upper  base =  r

And we have that

V =  (pi/3) height  ( r^2   + Rr   + R^2)

2401 pi  = (pi/3)  21  *  ( r^2 + 14r + 14^2)

2401/7  =  r^2 + 14r + 196

343  = r^2  + 14r+ 196

r^2 + 14r   - 147 =   0

(r + 21) ( r - 7) = 0

r - 7 =  0    

r = 7(cm)   =  the  upper base

Lateral surface area =    pi *slant height  *  ( R + r)

slant height =   sqrt   [  (R-r)^2  + h^2  ]     =   sqrt  [ (14 - 7)^2 + 21^2 ]  =  sqrt [ 49 + 441] = sqrt [ 490] =

7sqrt (10)

Lateral surface area =    pi * 7sqrt (10)  *  ( 14 + 7)  =  147sqrt (10)  ≈  1460 cm^2 

The volume of a conical frustum is 2401π cu. cm. If the radius of the lower base is 14 cm and the altitude is 21-cm.

Calculate the lateral area of the conical frustum. *