Consider that the Volume of a cone (V), which has a height (h) and radius (r) is given by,
[tex]V=\frac{1}{3}\pi r^2h[/tex]Figure-1
Given that the radius is 8 in. and the height is 14 in. the volume is calculated as,
[tex]\begin{gathered} V_1=\frac{1}{3}\pi(8)^2(14) \\ V_1=\frac{896}{3}\pi \\ V_1=938.289 \end{gathered}[/tex]So the volume of this cone is 938.289 cubic inches approximately.
Figure-2
Given that the radius is 9 in. and the height is 13 in. the volume is calculated as,
[tex]\begin{gathered} V_2=\frac{1}{3}\pi(9)^2(13) \\ V_2=351\pi \\ V_2=1102.699 \end{gathered}[/tex]So the volume of this cone is 1102.699 cubic inches approximately.
Figure-3
Given that the radius is 7 in. and the height is 10 in. the volume is calculated as,
[tex]\begin{gathered} V_3=\frac{1}{3}\pi(7)^2(10) \\ V_3=\frac{490}{3}\pi \\ V_3=513.127 \end{gathered}[/tex]So the volume of this cone is 513.127 cubic inches approximately.
Figure-4
Given that the radius is 6 in. and the height is 12 in. the volume is calculated as,
[tex]\begin{gathered} V_4=\frac{1}{3}\pi(6)^2(12) \\ V_4=144\pi \\ V_4=452.389 \end{gathered}[/tex]So the volume of this cone is 1102.699 cubic inches approximately.
Observe the volume values obtained for all four cones,
[tex]\begin{gathered} 452.389<513.127<938.289<1102.699 \\ \Rightarrow V_4Thus, the order of least to greatest volume is, figures 4, 3, 1, 2 respectively.