Question

the circumference of the base of a cone is 220/7cm . its slant height is 13 cm .find the volume of the cone

Answer 1

Hello friends!!

Here is ur answer :

First, the formula used in this question :

Circumference of base :

$2\pi r$


Height of cone :
$\sqrt{ {l}^{2} - {r}^{2} }$


Volume of cone :

$\frac{1}{ 3} \pi {r}^{2} h$


Now come to the question :

Circumference of base of a cone = 220 / 7 cm

We have to find radius of cone.

Let the radius be r.

$2\pi r = \frac{220}{7}$

$\pi = \frac{22}{7}$

$2 \times \frac{22}{7} \times r = \frac{220}{7}$


$r = \frac{220}{7} \times \frac{7}{22} \times \frac{1}{2}$


$r = \frac{10}{2}$


$r = 5$

Therefore, radius r of cone = 5 cm

Slant height l of cone = 13 cm

We have to find height of cone.

Let the height be h.

Using formula,

${l}^{2} = {r}^{2} + {h}^{2}$


${(13)}^{2} = {(5)}^{2} + {h}^{2}$


$169 = 25 + {h}^{2}$


${h}^{2} = 169 - 25$

${h}^{2} = 144$


$h = \sqrt{144}$



$h = 12$


Height h of cone = 12 cm


Volume of cone :

$= \frac{1}{3} \times \frac{22}{7} \times {(5)}^{2} \times 12$



$= 1 \times \frac{22}{7} \times 25 \times 4$


$= \frac{2200}{7}$


$= 314.285714 \: \: {cm}^{3}$


HOPE IT HELPS YOU..