A cone has a slant height of 34 cm and the radius is 16 cm. What is the exact volume of the cone?

##2560pi## cubic units.
If the cone has a slant height of ##color(orange)(s=34)## and a radius of ##color(red)(r=16)##
then its height is (using the Pythagorean Theorem)
##color(white)(XXX)color(blue)(h)=sqrt(color(orange)(34)^2-color(red)(16)^2)=color(blue)(3)0##
The volume of a cone is given by the formula:
##color(white)(XXX)v=1/3picolor(red)(r)^2color(blue)(h)##
In this case
##color(white)(XXX)v=1/3*pi*color(red)(16)^2*color(blue)(30)##
##color(white)(XXXX)=2560pi##