The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm.

Dimension of the metal block is $2.25 \mathrm{~m} \times 1.5 \mathrm{~m} \times 27 \mathrm{~cm}$, i. e., $225 \mathrm{~cm} \times 150 \mathrm{~cm} \times 27 \mathrm{~cm}(\because 1 \mathrm{~m}=100 \mathrm{~cm})$.

Volume of the metal block $=225 \times 150 \times 27=911250 \mathrm{~cm}^{3}$

This metal block is melted and recast into cubes each of side $45 \mathrm{~cm}$.

Volume of a cube $=(\text { side })^{3}=45^{3}=91125 \mathrm{~cm}^{3}$

$\therefore$ The number of such cubes formed from the metal block $=\frac{\text { volume of the metal block }}{\text { volume of } a \text { metal cube }}=\frac{911250 \mathrm{~cm}^{3}}{91125 \mathrm{~cm}^{3}}=10$