The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.

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In this problem use π=3.14.

This question was asked in 2012 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 823, exercise 17C, problem number 13

Solution

given data

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Surface area of the frustum = π(R+r)l +πR² +πr²

=π(R²+r²+l[R+r])

= [33²+27²+10[33+27]]π

= [1089+729+1060]π

= 2418×3.14

= 7592.52 cm²

∴ total surface area of frustum is 7592.52 cm²