Given that,
\(h_1 : h_2 = 1: 2 \) and \(2 \pi r_1 : 2 \pi r_2 = 3: 4\)
\(i.e., r_1 : r_2 = 3:4\)
Therefore,
The ratios of volume of their cones will be
\(v_1 :v_2 = \frac {1}{3} \pi \,r ^2 _1 h_1 : \frac {1}{3} \pi r ^2 _2 h_2\)
\(\frac {V_1}{V_2} =\cfrac {\frac {1}{3}\pi \,r^2_1 h_1}{\frac {1}{3}\pi \,r^2_1 h_2}\)
\(=\left( \frac {r_1}{r_2}\right)^1 \times \left(\frac {h_1}{h_2}\right)\)
\(\frac {V_1}{V_2} = \left( \frac {3}{4}\right)^2 \times \left(\frac {1}{2}\right)\)
\(=\frac {9}{32}\)
\(V_1 : V_2 = 9: 32\)
