This is the important problem, in this problem use π = 3.14, Problem from RS Aggarwal book, Problem number 2, chapter volume and surface area of solid, Exercise 17 c

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# The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area.

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solution

given data

Height = 8 cm

Base radii, R= 18 cm and r = 12 cm

the slant height

l = √[(R -r)² + h²]

= √[(18-12 )² + 8²]

= √ 6² +8²

= √36 + 64

= √100

l = 10 cm

Total surface area of the solid frustum = π(R+r)l +πR² +πr²

= 3.14 × ( 18 + 12 ) ×10 + [3.14 ×18²]+[ 3.14 ×12²]

= 3.14 × ( 300 + 324 + 144 )

= 3.14 × 768

= 2411.52 cm²