Q13 of 24 Page 227

If each of radius of a cone is increased by twice of its length, then the volume of it will be

In 1st case,


Base radius = r


Height = h


∴ Volume, x = πr2h/3


In 2nd case,


Base radius = 2r


Height = h


∴ volume, y = π(2r)2×h/3 = 4πr2h/3



⇒ y/x = 4


⇒ y = 4x


∴ The volume will be 4 times.

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Let us write whether the following statements are true or false:

(i) If the length of the base radius of a right circular cone is decreased by half and its height is increased by twice of it then the volume remains the same.


(ii) The height, radius and slant height of a right circular cone are always the three sides of a right-angles triangles.