a cone and a sphere have the same volume. the height of the cone is 96 units. what would be the values for the radius of the cone and the sphere?

The volume [tex]V_c[/tex] of a cone  with base radius [tex]r_c[/tex] and height [tex]h_c[/tex] is[tex]V_c = \dfrac{1}{3}\pi r_c^2 h_c[/tex]Similarly, the volume [tex]V_s[/tex] of a sphere with radius [tex]r_s[/tex] is[tex]V_s = \dfrac{4}{3}\pi r_s^3[/tex]We know that [tex]V_c=V_s[/tex] and that [tex]h_c=96[/tex]So, we can set up the following equation:[tex]\dfrac{96}{3}\pi r_c^2=\dfrac{4}{3}\pi r_s^3[/tex]We can simplify the common denominator 3, and pi appearing on both sides:[tex]96r_c^2=4r_s^3[/tex]We can divide both sides by 4:[tex]24r_c^2=r_s^3[/tex]Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.