Question

COne.
If the volume of a right circular cone is 100+ cm and height is 12cm., then let us write by
calculating, the slant height of the cone.
slant height of the tent​

Answer 1

Given :

Volume of cone, v = 100 cm

Height of cone, h = 12 cm

To find :

Slant height of cone , l = ?

Formula :

$volume \: \: of \: \: cone \: \: = \frac{1}{3} \pi {r}^{2} h$

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

Solution :

Volume of cone = 100

$\frac{1}{3} \pi {r}^{2} h = 100$

$\pi {r}^{2} \times 12 = 300$

( by cross multiplying )

$\pi {r}^{2} = \frac{300}{12 }$

$\pi {r}^{2} = 25$

${r}^{2} = \frac{25}{\pi}$

$r = \sqrt{ \frac{25}{\pi} } \: \: \: \: \: \: \: cm$

Then ,,,,

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

$l = \sqrt{ {( \sqrt{ \frac{25}{\pi} } )}^{2} + {(12)}^{2} }$

$l = \sqrt{ \frac{2 5}{\pi} + 144}$

$l = \sqrt{ \frac{25 + 144\pi}{\pi} }$

$l = \sqrt{ \frac{25 + 144 \times \frac{22}{7} }{ \frac{22}{7} } }$

$l = \sqrt{25 + 144 \times \frac{22}{7} \times \frac{7}{22} }$

$l = \sqrt{25 + 144}$

$l = \sqrt{169}$

$l = 13 \: \: \: \: cm$

Therefore ,,,

The measure of slant height is 13cm ......