Question

14. The curved surface area of a cone, with the radius of its base as 35 cm, is 4070 cm2.find
its volume.

Answer 1

Given :

• Radius of Cone is 35 cm .
• Curved Surface Area of Cone is 4070 cm² .

To Find :

• Volume of Cone .

Solution :

Firstly we will find Slant Height of Cone :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{4070=\dfrac{22}{{\cancel{7}}}\times{{\cancel{35}}}\times{l}}$

$\longmapsto\tt{4070=22\times{5}\times{l}}$

$\longmapsto\tt{4070=110\:l}$

$\longmapsto\tt{l=\dfrac{{\cancel{407}}{\not{0}}}{{\cancel{11}}{\not{0}}}}$

$\longmapsto\tt\bf{l=37\:cm}$

Also ,

We will find Height of Cone :

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

$\longmapsto\tt{{(37)}^{2}={(h)}^{2}+{(35)}^{2}}$

$\longmapsto\tt{1369={(h)}^{2}+1225}$

$\longmapsto\tt{1369-1225={(h)}^{2}}$

$\longmapsto\tt{\sqrt{144}=h}$

$\longmapsto\tt\bf{12\:cm=h}$

Now ,

For Volume of Cone :

Using Formula :

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

Putting Values :

$\longmapsto\tt{\dfrac{1}{{\cancel{3}}}\times\dfrac{22}{{\cancel{7}}}\times{{\cancel{35}}}\times{35}\times{{\cancel{12}}}}$

$\longmapsto\tt{22\times{5}\times{35}\times{4}}$

$\longmapsto\tt\bf{15400\:{cm}^{3}}$

So , The Volume of Cone is 15400 cm³ .