Q13 of 24 Page 227

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.

(i) false


In 1st case,


Base radius = r


Height = h


∴ Volume, x = πr2h/3


In 2nd case,


Base radius = r/2


Height = 2h


∴ volume, y = π(r/2)2×2h/3 = πr2h/6


∴ x ≠ y


∴ volume will not remain same


(ii) True


The height is equivalent to the perpendicular of a right-angle triangle.


The radius is equivalent to the base and the slant height is equivalent to the hypotenuse.


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