Question

The volume of right circular cone is 2200/7 cm^3 and its height 12 cm. Find its slant height.​

Answer 1

Given :

• Volume of Cone is 2200/7 cm³ .
• Height of Cone is 12 cm .

To Find :

• Slant Height of Cone .

Solution :

Firstly we will find Radius :

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

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cylinder=\dfrac{1}{3}\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{\dfrac{2200}{7}=\dfrac{1}{3}\times\dfrac{22}{7}\times{{r}^{2}}\times{12}}$

$\longmapsto\tt{\dfrac{2200}{7}=\dfrac{264{r}^{2}}{21}}$

$\longmapsto\tt{{r}^{2}=\dfrac{2200\times{21}}{7\times{264}}}$

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

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

$\longmapsto\tt\bf{r=5\:cm}$

Radius of Cone is 5 cm ..

Now ,

For Slant Height :

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

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

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

$\longmapsto\tt{l=\sqrt{139}}$

$\longmapsto\tt\bf{l=13\:cm}$

So , The Slant Height of Cone is 13 cm ...