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