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