Question

A right triangle whose sides are 3cm,4cm and 5cm is revolved about the sides containing the right angle in two ways. Find the difference of volumes of the cones so formed.

Answer:

Difference of their volumes is 4π cubic cm.

Case 1(The triangle is revolved about the side of length 3cm):
The height of the cone becomes 3cm and the base radius becomes 4cm.
Case 2(The triangle is revolved about the side of length 4cm):
The height of the cone becomes 4cm and the base radius becomes 3cm.
Therefore, the difference of their volumes:
= (1/3)π*3*3*4 - (1/3)π*4*4*3
= (1/3)π*4*3(4-3) [Taking (1/3)π*4*3 common]
= 4π*1 = 4π cubic cm.


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