Question

If the Volume of a right circular cone is 100 π cm³ and height is 12cm, then let us write by calculating the slant height of the cone.​

Answer 1

Given :

• Volume of Cone = 100π
• Height of Cone = 12cm

To Find :

• Slant Height of the Cone

Solution :

Firstly we will find the Radius of Cone :

$\longmapsto\tt{Volume=100\pi}$

$\longmapsto\tt{Height=12cm}$

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cone=\pi{{r}^{2}\dfrac{h}{3}}}$

Putting Values :

$\longmapsto\tt{100{\cancel{\pi}}={\cancel{\pi}}{{r}^{2}\dfrac{h}{3}}}$

$\longmapsto\tt{100={r}^{2}\times\dfrac{\cancel{12}}{\cancel{3}}}$

$\longmapsto\tt{100=4{r}^{2}}$

$\longmapsto\tt{{r}^{2}=\cancel\dfrac{100}{4}}$

$\longmapsto\tt{{r}^{2}=\sqrt{25}}$

$\longmapsto\tt\bold{r=5cm}$

So , The Radius of Cone is 5cm...

Now :

For Slant Height :

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

$\longmapsto\tt{{l}^{2}=\sqrt{{(12)}^{2}+{(5)}^{2}}}$

$\longmapsto\tt{{l}^{2}=\sqrt{144+25}}$

$\longmapsto\tt{{l}^{2}=\sqrt{169}}$

$\longmapsto\tt\bold{l=13cm}$

Therefore, Slant height (l) of the cone is 13cm..