In this problem use π = 22/7

Problem from RS Aggarwal book, problem number 6, page number 823, exercise 17C, chapter volume and surface area of solid.

Chapter Mensuration

Deepak BoraNewbie

# 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 capacity and total surface area.

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solution

given data

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Height = h = √[l²-[R-r]²]

=√[10²-[33-27]²]

=√[100-6²]

=√[100-36]

=√64

h =8 cm

Capacity of the frustum =[1/3] π h [R²+r²+rR]

=[1/3]×[22/7]× 8 [33²+27²+[33×27]]

∴ Capacity of the frustum = 22704 cm³

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

=[22/7] [33²+27²+(33+27)10]

=122×24187

=7599.43 cm²

∴ Surface area of the frustum is 7599.43 cm²