# The perimeters of the ends of the frustum of a cone are 207.24 cm and 169.56cm.if the height of the frustum be 8 cm,find the whole surface area of the frustum. (use .3.14)

1
by ramnihal

2016-03-10T10:46:05+05:30

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Perimeter of 1st end = 2 π R

⇒ 207. 24 cm = 2 x 3.14 x R
207.24 cm =  6.28 cm x R
33 = R
i .e R = 33

Perimeter or 2nd end = 2 π r
169. 56 cm = 2 x 3.14 x r
169. 56 cm  = 6.28 cm x r
27 cm = r
i .e. , r = 27 cm

So ,
We need to find slant height first .

R = 33 cm
r = 27 cm
H = 8 cm

⇒ slant height =

⇒ Slant height =

⇒ Slant height =

⇒ Slant height = 20 .59 , round it to 20.6 cm

⇒Total surface area = π ( r + R ) l + π R² + π r ²

⇒ Total surface area = 3.14 ( 27 + 33 ) 20.6 + 3.14 ( 33)² + 3.14(27)²

Total surface area = 3.14 ( 60 ) (20.6) + 3.14 ( 1089 ) + 3.14 ( 729)

⇒ Total Surface area =  3881.04 + 3419.46 + 2289.06

⇒ Total Surface area = 9589.56 cm²

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