Question

Find the slant height of a frustum cone whose top radius is $12m$ and bottom radius is $10m$. The height of the cone is $13m$.

Answer 1

Solve for the slant height of cone:

Let $h$ be the height, $r$ be the radius and $l$ be its slant height.

Here, $h=13m$, $r_2=12m$ and $r_1=10m$.

Relationship between the three quantities is,

$\begin{array}{rcl}\mathit{l}& \mathbf{=}& \sqrt{{\mathbf{h}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}{\mathbf{r}}_{\mathbf{2}}\mathbf{-}{\mathbf{r}}_{\mathbf{1}}\mathbf{)}}^{\mathbf{2}}}\end{array}$

Thus,

$\begin{array}{rcl}l& =& \sqrt{{13}^2+{\left(12-10\right)}^2}\\ & =& \sqrt{169+4}\\ & =& \sqrt{173}m\end{array}$

Hence, the slant height of a frustum cone is $\sqrt{173}m$.