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Define “Regular cone”. Deduce formula for slant height of a regular cone.

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A solid having a circular base and vertex above the centre of circular base is called a regular cone. 

A → Vertex 

‘O’ centre of ground 

OB is the radius of cone (r) and

OA is the height of cone (h) 

AB is slant height (l) 

Now ΔAOB is a right angled triangle. 

Where ∠AOB = 90 and AB is hypotenuse. 

Then from Pythagoras theorem

AB2 = OA2 + OB2 = r2 + h2 

∴ AB = \(\sqrt{r^2+h^2}\)

∴ Slant height (l) = \(\sqrt{r^2+h^2}\)

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