Question

A metal block with dimensions 240 cm by 160 cm
by 75 cm is melted and recast into cubes each of 48
cm. How many cubes are formed ?​

Answer 1

Given:-

• Length (l) = 240 cm

• Breadth (b) = 160 cm

• Height (h) = 75 cm

• Side of cube (a) = 48 cm

To Find:-

• Number of cubes when the metal block is melted.

Formula used:-

• ${\bf{\boxed{Volume\:of\: Cuboid= l\times b\times h}}}$

• ${\bf{\boxed{Volume\:of\: Cube= a^3}}}$

Solution:-

Firstly,

$\sf :\implies\:Volume\:of\: Block= l\times b\times h$

$\sf :\implies\:Volume\:of\: Block= 240\times 160 \times 75$

$\bf :\implies\:Volume\:of\: Block= 28,80,000cm^3$

Now,

$\sf :\implies\:Volume\:of\: Cube= a^3$

$\sf :\implies\:Volume\:of\: Cube= 48^3$

$\bf :\implies\:Volume\:of\: Cube= 1,10,592cm^3$

Finally,

$\sf :\implies\:No. \: of \:Cubes\:formed= \dfrac{Volume\:of\:Block}{Volume\:of\:Cube}$

$\sf :\implies\:No. \: of \:Cubes\:formed= \dfrac{28,80,000}{1,10,592}$

$\sf :\implies\:No. \: of \:Cubes\:formed= 26.041$

Hence, 26 Cubes will be formed if we melt the given block.

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