Question

derive frustum with figure...

Answer 1

From the figure, we have, the total height H’ = H+h and the total slant height L =l1 +l2. The radius of the cone = R and the radius of the sliced cone = r. Now the volume of the total cone = 1/3 π R2 H’ = 1/3 π R2 (H+h)

The volume of the Tip cone = 1/3 πr2h. For finding the volume of the frustum we calculate the difference between the two right circular cones, this gives us

= 1/3 π R2 H’ -1/3 πr2h
= 1/3π R2 (H+h) -1/3 πr2h
=1/3 π [ R2 (H+h)-r2 h ]

Now on seeing the whole cone with the sliced cone, we come to know that the right angle of the whole cone Δ QPS  is similar to the sliced cone Δ QAB. This gives us, R/ r = H+h / h ⇒ H+h = Rh/r . Substituting the value of H+h in the formula for the volume of frustum we get,

=1/3 π [ R2 (Rh/r)-r2 h ] =1/3 π  [R3h/r-r2 h )]
=1/3 π h (R3/r-r2 )  =1/3 π h (R3-r3 / r)

The Volume of Frustum of Cone = 1/3 π h [(R3-r3)/ r]

Answer 2

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