Question

Question 3
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Answer 1

False.
On rotating a right-angled triangular lamina AOB about OA, it generates a cone. The point A is the vertex of a cone. Its base is a circle with centre O and radius OB. The length OA is the height of the cone and the length AB is called its slant height.


Clearly, $\angle AOB={90}^{\circ }$

Let the radius of the base = r units, height = h units

Slant height = l units
Then,

$l^2=h^2+r^2\Rightarrow l=\sqrt{h^2+r^2}$

Hence, in a right circular cone; height, radius and slant height are always be the sides of a right triangle.