The radii of the ends of a frustum of a cone 45cm high are 28 cm and 7cm. Find its volume, the curved surface area, and the total surface area (take π=227).
The frustum can be viewed as a difference of two right circular cones OAB and OCD . let the height of the cone OAB be h1 and its slant height l1
i.e., OP=h1 and OA=OB=l1.
Let h2 be the height of cone OCD and l2 its Slant height .
We have r1=28cm , r2=7cm and the height of frustum (h) =45cm
Since the triangles OPB and OQD are similar , we have
From (i) and (ii) h2=15cm and h1= 60 cm.
now, the volume of the frustum = volume of the cone OAB – volume of the cone OCD
The respective slant height l2and l1 of the cones OCD and OAB are given by
Thus, the curved surface area of the frustum = πr1l1−πr2l2
Now, the total surface of the frustum = curved surface area + π(r1)2+π(r2)2