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The formula to find the slant height of the cone isA) $l = \sqrt {{h^2} - {r^2}}$B) $l = \sqrt {{h^2} + {r^2}}$C) $l = \sqrt {h + {r^{}}}$D) $l = \sqrt {{h^{}} - r}$

Last updated date: 28th May 2024
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Here in the above image we have AC is the slant height i.e. $l$. AB is the vertical height of the cone $(h)$ and BC is the radius i.e. $r$.
Now the formula of the slant height of the cone is $l = \sqrt {{h^2} + {r^2}}$.
Hence the correct option is (B) $l = \sqrt {{h^2} + {r^2}}$.
Now we can apply this formula whenever we have to find the slant height of the cone. Let us take an example. The height and base of a cone is $8m$ and $12m$. Calculate its slant height. Now by applying the above formula we have $h = 8$ . We should note that we have a base which is diameter , so the radius is $\dfrac{d}{2} = \dfrac{{12}}{2} = 6$. So we have $r = 6$. Now by applying the formula we have $l = \sqrt {{8^2} + {6^2}}$. On solving we have $l = \sqrt {64 + 36} = \sqrt {100}$. It gives us a slant height of $10$.