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.]
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−(R−r)2=√102−(33−27)2=√102−(6)2=√100−36=√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