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

1 Answer
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

thereforeThe slant height of the cone is 8