Q20 of 31 Page 1

The perimeters of the ends of the frustum of a cone are 207.24 cm and 169.56 cm. If the height of the frustum be 8 cm, find the whole surface area of the frustum. (Use π= 3.14)

Let r, R be radii of frustum (R>r) and h be the height of frustum.


Formula


Total surface area of frustum = π(R2 + r2 + (R + r)l)


Where, l is the slant height of frustum.


And


Perimeter of circular cylinder = 2πr


Given


Perimeter of bigger end = 207.24 cm


⇒ 2πR = 207.24


⇒ 2 × 3.14 × R = 207.24


⇒ R = 33 cm


Perimeter of smaller end = 169.56 cm


⇒ 2πr = 169.56


⇒ r = 27 cm


Height, h = 8 cm


Slant height,



Putting values in formula, we get


Total surface area = π(332 + 272 + (33 + 27)10)


= 3.14(1089 + 729 + 600)


= 7592.53 cm2


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