a.
Consider that the volume (V) of a cone with radius 'R' and height 'H' is given by,
[tex]V=\frac{1}{3}\pi R^2H[/tex]Substitute the values,
[tex]\begin{gathered} V=\frac{1}{3}\pi(4)^2(3) \\ V=16\pi \end{gathered}[/tex]Therefore, option b is the correct choice.
b.
Consider that the volume (V') of a cylinder with radius 'R' and height 'H' is given by,
[tex]V^{\prime}=\pi R^2H[/tex]Solve for the ratio of volume of cone to that of cylinder as,
[tex]\frac{V}{V^{\prime}}=\frac{(\frac{1}{3}\pi R^2H)}{(\pi R^2H)}=\frac{1}{3}[/tex]Therefore, option c is the correct choice.
