ANSWER
The height of the larger cone is 3cm
EXPLANATION
Since the two cones are similar we can use the scale factor to determine the height of the larger cone.
It was given that, the volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³.
The scale factor for the volume is
[tex] {k}^{3} = \frac{27}{8} [/tex]
The scale factor for the length is
[tex]k = \sqrt[3]{ \frac{27}{8} } [/tex]
[tex]k = \frac{3}{2} [/tex]
To find the height of the larger cone, we multiply by
[tex] h = \frac{3}{2} \times 2 = 3[/tex]
