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Question

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. [Take π=22/7.]

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Solution

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Using the formula for the height of a frustum:

Height =h=l2(Rr)2=102(3327)2=102(6)2=10036=64=8 cm

Capacity of the frustum

=13πh(R2+r2+Rr)=13×227×8(332+272+33×27)=22×83×7×2709=22704 cm3

Surface area of the frustum

=πR2+πr2+πl(R+r)=π[R2+r2+l(R+r)]=227[332+272+10(33+27)]=227[1089+729+10(60)]=22×24187=7599.43cm2


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