Answer:
3
Step-by-step explanation:
Let V and v be volumes of two similar cones.
so R/r=H/h
V=1/3π R²H
v=1/3πr²h
[tex]\frac{V}{v} =\frac{\pi R^2H }{\pi r^2h } =(\frac{R}{r} )^2(\frac{H}{h} )=(\frac{H}{h} )^3\\\frac{27}{8} =(\frac{H}{2} )^3\\\frac{3^3}{2^3} =(\frac{H}{2} )^3\\(\frac{3}{2} )^3=(\frac{H}{2} )^3\\\frac{H}{2} =\frac{3}{2} \\H=\frac{3}{2} \times 2=3[/tex]
