Question

l=√r2 +h2 then l
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Answer 1

Answer:

hypotenuse of triangle

Step-by-step explanation:

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Answer 2

$\Large\textrm{Formulae}$

The formula of,

$\cdots\longrightarrow\boxed{\rm{l=\sqrt{r^{2}+h^{2}}}}$

This explains the slant height of a cone from the Pythagorean theorem.

$\Large\textrm{Explained}$

Let us say,

• $\rm{l}$ is the slant height
• $\rm{r}$ is the radius
• $\rm{h}$ is the height

If we cut the cone, we would get the pieces in half.

The section would be a right triangle. As we know the Pythagorean theorem, we write it as $\rm{l^{2}=r^{2}+h^{2}}$.

We know all three lengths must be positive.

Taking square root on both sides,

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

We know,

$\rm{\cdots\longrightarrow\boxed{\rm{\sqrt{x^{2}}=|x|}}}$

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

We know,

$\rm{\cdots\longrightarrow\boxed{\rm{|x|=x\ for\ x>0}}}$

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

Hence proven.

Hope it helped. Keep learning!