ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
Here you have to Write whether the following statements are true or false
Give the answer as asked in this question part wise.
This is the Question Number 01, Exercise 17.2 of M.L Aggarwal.
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Write whether the following statements are true or false. Justify your answer. (i) If the radius of a right circular cone is halved and its height is doubled, the volume will remain unchanged. (ii) A cylinder and a right circular cone are having the same base radius and same height. The volume of the cylinder is three times the volume of the cone. (iii) In a right circular cone, height, radius and slant height are always the sides of a right triangle.
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(i)Volume of cone = (1/3)r2h
If radius is halved and height is doubled, then volume = (1/3)(r/2)2 2h = (1/3)r2h/2
If the radius of a right circular cone is halved and its height is doubled, the volume will be halved.
So given statement is false.
(ii)Radius of cylinder = radius of cone
Height of cylinder = height of cone
Volume of cylinder = r2h
Volume of cone = (1/3)r2h
The volume of the cylinder is three times the volume of the cone.
So given statement is true.
(iii)In a right circular cone,
l2 = h2+r2
In a right circular cone, height, radius and slant height are always the sides of a right triangle.
So given statement is true.