A solid metal block is 25 cm long,15 cm wide,10 cm high.it is cut into solid cubical blocks of the same size.Find the number of cu

[tex]\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}[/tex]

• [tex] \sf a \: metal \: block \: has : [/tex]
• [tex] \sf h(height) = 10cm[/tex]
• [tex] \sf l(length) = 25cm[/tex]
• [tex] \sf b(breadth) = 15cm[/tex]

[tex]\color{red}\huge{\underline{\underline{\bf TO\:FIND\dag}}}[/tex]

• [tex] \sf no. \: of \: cubical \: blocks (5cm) \: that \: can\\ \sf\: be \: formed[/tex]

[tex]\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}[/tex]

[tex] \blue{ \boxed{volume \: of \: cuboid = l \times b \times h}}[/tex]

[tex] \implies \sf vol. \: of \: cuboid = 25 \times 15 \times 10[/tex]

[tex] \therefore \sf vol. \: of \: cuboid = 3750 \: {cm}^{3} [/tex]

[tex] \blue{ \boxed{volume \: of \: cube = {a}^{3} }}[/tex]

[tex] \implies \sf vol. \: of \: cube = {5}^{3} [/tex]

[tex] \therefore \sf vol. \: of \: cube = 125 \: {cm}^{3} [/tex]

[tex] \purple{\bold{ \sf let \: the \: no. \: of \: cubes \: formed \: be \: \purple{‘x’} }}[/tex]

[tex] \implies \sf x = \frac{vol. \: of\: cuboid}{vol. \: of \: cube} [/tex]

[tex]\implies \sf x = \frac{ \cancel{3750}}{ \cancel{125} }[/tex]

[tex] \orange{ \therefore \sf x = 30 }[/tex]

[tex] \therefore \sf 30 \: cubical \: blocks \: can \: be \: formed \: from \: solid \: \\ \sf metal \: block.[/tex]