In a right circular cone, \(\sqrt{(l+r)(l-r)}\) =(A) slant height (

1.	In a right circular cone, \(\sqrt{(l+r)(l-r)}\) =(A) slant height (B) vertical height (C) radius of the base (D) diameter of the base
Answer» Correct option is: (B) vertical height In right circular cone, we have r = Radius of base of the cone, h = Vertical height of the cone l = slant height of the cone Now, \(\sqrt{(l + r)(l - r)}\) = \(\sqrt {l^2-r^2}\) (\(\because\) (a+b) (a-b) = \(a^2-b^2\)) = \(\sqrt {h^2}\) (\(\because\) \(l^2 = r^2 + h^2 = l^2 -r^2 = h^2\)) = h which is vertical height of the right circular cone. Correct option is: (B) vertical height

In a right circular cone, \(\sqrt{(l+r)(l-r)}\) =(A) slant height (B) vertical height (C) radius of the base (D) diameter of the base

Answer»

Correct option is: (B) vertical height

In right circular cone, we have

r = Radius of base of the cone,

h = Vertical height of the cone

l = slant height of the cone

Now, \(\sqrt{(l + r)(l - r)}\) = \(\sqrt {l^2-r^2}\) (\(\because\) (a+b) (a-b) = \(a^2-b^2\))

= \(\sqrt {h^2}\) (\(\because\) \(l^2 = r^2 + h^2 = l^2 -r^2 = h^2\))

= h which is vertical height of the right circular cone.

Correct option is: (B) vertical height