A tent is made in the form of a conic frustum surmounted by a cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively and the height is 24 m. If the height of the tent is 28 m, find the quantity of canvas required.
Let h be the height of the frustum and r1 and r2 be the radii of its circular bases.
We have h=24m,r1=10m,r2=3m
l= slant height of the frustum
⇒l=√(r1−r2)2+h2=√(10−3)2+242=25m
for cone VA'B', we have
l2= slant height =√O′B′2+VO′2=√32+42=5m
Quantity of canvas required
= lateral surface area of frustum + lateral surface area of cone VA′B′
=π(r1−r2)l+πr2l2
={π(10+3)×25+π×3×5}m2
=(325π+15π)m2
=340π m2