If the lateral area of a cone is 24pi and the radius is 3, what is the slant height?

May 27, 2017

The slant height of the cone is $8$ units or whatever the original "unit" used in the formulation of this answer used.

Explanation:

Lateral area of cone=pir sqrt( h^2+r^2

A=pir sqrt( h^2+r^2

24 pi=pi3 sqrt( h^2+3^2

Now we can use some simple algebra to find $h$.

24 cancel(pi)=cancel(pi)3 sqrt( h^2+3^2

24 =3 sqrt( h^2+3^2

8 = sqrt( h^2+3^2

${8}^{2} = {h}^{2} + {3}^{2}$

$64 = {h}^{2} + 9$

$64 = {h}^{2} + 9$

$55 = {h}^{2}$

h = sqrt(55

$h = 7.416$

We can now use Pythagoras theorem to find the slant height.

${a}^{2} + {b}^{2} = {c}^{2}$

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

${3}^{2} + {7.416}^{2} = {s}^{2}$

$9 + 55 = {s}^{2}$

s = sqrt(64

$s = 8$

$\therefore$The slant height of the cone is $8$