Question

find the volume of the cone whose slant height is 17 cm and base radius is 8 cm

Answer 1

Hey!!
Thanks for the question!!

Here is the answer..

Volume of cone = ?
Slant height = 17 cm
Radius = 8 cm
Height = ?

Slant Height of cone ( l ) =
$\sqrt{r {}^{2} + h {}^{2} }$
$( 17) {}^{2} =( 8) {}^{2} +( h) {}^{2}$
$(17) {}^{2} -( 8 ){}^{2} = (h) {}^{2}$
$289 - 64 = h {}^{2} \\ 225 = h {}^{2} \\ 15 = h$

Hence, we got height.
$\text{h \: = 15 \: cm}$

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

$= \frac{1}{3} \times 3.14 \times 8 {}^{2} \times 15$

$= \frac{1}{3} \times 3.14 \times 64 \times 15$

$= 3.14 \times 64 \times 5$

$= {3.14 \times 320}$

$= \textbf{1004.8}$

Hence,
The volume of cone whose slant height is 17 cm and base radius is 8 cm is 1004.8 cu.cm.

I hope my answer helped!!

Answer 2

HEY MATE HERE IS YOUR ANSWER

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

Slant height = 17cm
Radius = 8cm

First we have to find height of cone to find the volume

${h}^{2} =\sqrt{ {l}^{2} - {r}^{2} }$
${h}^{2} = \sqrt{ {17}^{2} - {8}^{2} }$

${225} = {h}^{2}$
$h = 15$
Volume of cone =
$\frac{1}{3} \pi {r}^{2}h$
$\frac{1}{3} \times \frac{22}{7} \times 8 \times 8 \times 15$
$= 1005.71 \: {cm}^{3}$

Hope it will help you