Let the number of cones be  n.

Let the radius of the sphere be  r_s = 6 cm

Radius of a cone be  r_c = 2 cm

And height of the cone be  h = 3 cm

Volume of sphere = n ( Volume of a metallic cone )

$$\begin{gathered} \Rightarrow \frac{4}{3} \mathrm{\pi } {{\mathrm{r}}_{\mathrm{s}}}^3 = \mathrm{n} \left( \frac{1}{3} \mathrm{\pi } {{\mathrm{r}}_{\mathrm{c}}}^2 \mathrm{h} \right) \\ \Rightarrow \frac{4}{\cancel{3}} \cancel{\mathrm{\pi }} {{\mathrm{r}}_{\mathrm{s}}}^3 = \mathrm{n} \left( \frac{1}{\cancel{3}} \cancel{\mathrm{\pi }} {{\mathrm{r}}_{\mathrm{c}}}^2 \mathrm{h} \right) \\ \Rightarrow \frac{ 4 {{\mathrm{r}}_{\mathrm{s}}}^3}{{{\mathrm{r}}_{\mathrm{c}}}^2 \mathrm{h}} = \mathrm{n} \\ \Rightarrow \mathrm{n} = \frac{ 4 ( 6 {)}^3}{( 2 {)}^2 ( 3 )} \\ \Rightarrow \mathrm{n}= \frac{\cancel{4} \mathrm{x} 216}{\cancel{4} \mathrm{x} 3} \\ \Rightarrow \mathrm{n} = 72 \end{gathered}$$

Hence, the number of cones is  72.

$$\begin{gathered} - 3 ( \mathrm{x} - 7 ) \ge 15 - 7 \mathrm{x} > \frac{\mathrm{x} + 1}{3} \\ \Rightarrow - 3 ( \mathrm{x} - 7 ) \ge 15 - 7 \mathrm{x} \mathrm{and} 15 - 7 \mathrm{x} > \frac{\mathrm{x} + 1}{3} \\ \Rightarrow - 3 \mathrm{x} + 21 \ge 15 - 7 \mathrm{x} \mathrm{and} 45 - 21 \mathrm{x} > \mathrm{x} + 1 \\ \Rightarrow - 3 \mathrm{x} + 7 \mathrm{x} \ge 15 - 21 \mathrm{and} 45 - 1 > \mathrm{x} + 21 \mathrm{x} \\ \Rightarrow 4 \mathrm{x} \ge - 6 \mathrm{and} 44 > 22 \mathrm{x} \\ \Rightarrow \mathrm{x} \ge \frac{- 3}{2} \mathrm{and} 2 > \mathrm{x} \\ \Rightarrow \mathrm{x} \ge - 1.5 \mathrm{and} 2 > \mathrm{x} \\ \mathrm{The} \mathrm{solution} \mathrm{set} \mathrm{is} \left\{ \mathrm{x} : \mathrm{x} \in \mathrm{R}, - 1.5 \le \mathrm{x} < 2 \right\}. \end{gathered}$$

$( \mathrm{i} ) \mathrm{Scale} \mathrm{factor} \mathrm{k} = \frac{1}{300}$

Length of the model of the ship  =  k x Length of the ship

$$\begin{gathered} \Rightarrow 2 = \frac{1}{300} \mathrm{x} \mathrm{Length} \mathrm{of} \mathrm{the} \mathrm{ship} \\ \Rightarrow \mathrm{Length} \mathrm{of} \mathrm{the} \mathrm{ship} = 600 \mathrm{m} \end{gathered}$$

( ii ) Area of the deck of the model =  k²  x  Area of the deck of the ship

$$\begin{gathered} \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{the} \mathrm{deck} \mathrm{of} \mathrm{the} \mathrm{model} = {\left( \frac{1}{300} \right)}^2 \mathrm{x} 180,000 \\ = \frac{1}{90000} \mathrm{x} 180,000 \\ = 2 {\mathrm{m}}^2 \end{gathered}$$

( iii ) Volume of the model  =  k³ x  Volume of the ship

$$\begin{gathered} \Rightarrow 6.5 = {\left( \frac{1}{300} \right)}^3 \mathrm{x} \mathrm{Volume} \mathrm{of} \mathrm{the} \mathrm{ship} \\ \Rightarrow \mathrm{Volume} \mathrm{of} \mathrm{the} \mathrm{ship} = 6.5 \mathrm{x} 27000000 = 175500000 {\mathrm{m}}^3 \end{gathered}$$