Question
Write True or False and justify your answer in the following:
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Answer

True.

Solution:

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, $\angle\text{AOB}=90^\circ$

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

and slant height = l unit, then

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

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