The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of the side 45 cm. How many cubes are formed?

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#### Solution

\[\text { Dimension of the metal block is 2 . 25 m } \times 1 . 5 m \times 27 \text { cm, i . e . , 225 cm } \times 150 cm \times 27 cm ( \because 1 m = 100 cm) . \]

\[\text { Volume of the metal block = 225 }\times 150 \times 27 = 911250 {cm}^3 \]

\[\text { This metal block is melted and recast into cubes each of side 45 cm }. \]

\[\text { Volume of a cube = (side )}^3 = {45}^3 = 91125 {cm}^3 \]

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

Concept: Surface Area of a Cube

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