Question

If the slant height of a cone is 18.7 cm and the curved surface area is 602.8 cm², find the volume of cone. (???? = 3.14)

Answer 1

curved surface area of cone(S) = $\pi rl$

where, l is slant height

Hence, $r =S/\pi l$

r = 10.25 cm

volume of cone(v) = $\frac{1}{3} \pi r^{2} H$

And H can be given as $H =\sqrt{l^{2}-r^{2}}$

where,r=10.25 cm and H =15.64 cm

v = $1.643*10^{3} \pi$

v = $5.1624*10^{3} cm^{3}$

Answer 2

Dear Student,

Answer: Volume if cone = 1721.43 cm^ cube

Solution:

slant height of cone l = 18.7 cm

curved surface area of cone =
$\pi \times r \times l$
here l is slant height,and r is radius.

$602.8 = \frac{22}{7} \times 18.7 \times r \\ \\ r = \frac{602.8 \times 7}{22 \times 18.7} \\ \\ r = 10.25 \: cm$
Volume of cone=
$\frac{1}{3} \pi {r}^{2} h$
To calculate cone's volume,we first calculate height of cone,

we can use Pythagoras theorem

${l}^{2} = {h}^{2} + {r}^{2} \\ {h}^{2} = {l}^{2} - {r}^{2} \\ {h}^{2} = ( {18.7)}^{2} - ( {10.25)}^{2} \\ h = \sqrt{244.62} \\ h = 15.6 \: cm$

Volume of cone
$= \frac{1}{3} \times \frac{22}{7} \times ( {10.25)}^{2} \times 15.64 \\ \\ = \frac{22 \times 105.06 \times 15.64}{21} \\ \\ = 1721.43 \: {cm}^{3}$
Hope it helps you.