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##