The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum.

For the given frustum:


Slant height, l = 4cm


Perimeter of its circular ends = 18cm and 6cm


Let radius of larger and shorter ends be r’ and r’’ resp., then


Perimeter of larger circular end = 2 π r’ = 18 cm


⇒ π r’ = 9


Similarly, 2π r’’ = 6


⇒ π r’’ = 3


Curved surface of the frustum = π (r’ + r’’) × l


= (9 + 3) × 4


= 48 cm2


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