Mensuration and similarity Cone P has a volume of 108cm^3
Calculate the volume of 2nd come , Q , whose radius is double that of cone P and its height is one-third that of cone p
Here's my working ....
$$V_Q=\frac13 \pi (2r)^2 \cdot  \frac{h}{3}\\ 
                = \frac{4}{9} \pi r^2 h\\ 
                = \frac{1}{3}\pi r^2 h \cdot \frac{4}{3}$$ 
I don't understand why must I do this.

Hint:
In your equation, you already have $$V_Q = \left(\frac{1}{3}\pi r^2h\right) \cdot 43$$
You also know what the volume of cone $P$ is, and you know that it is equal to $\frac{1}{3}\pi r^2 h$
