##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##