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

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Answer 1 · 2017-05-27T03:46:43

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

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#

#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#