Question

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 cubical blocks,if each side measures 5 cm??

Answer 1

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

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

$\color{red}\huge{\underline{\underline{\bf TO\:FIND\dag}}}$

• $\sf no. \: of \: cubical \: blocks (5cm) \: that \: can\\ \sf\: be \: formed$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

$\blue{ \boxed{volume \: of \: cuboid = l \times b \times h}}$

$\implies \sf vol. \: of \: cuboid = 25 \times 15 \times 10$

$\therefore \sf vol. \: of \: cuboid = 3750 \: {cm}^{3}$

$\blue{ \boxed{volume \: of \: cube = {a}^{3} }}$

$\implies \sf vol. \: of \: cube = {5}^{3}$

$\therefore \sf vol. \: of \: cube = 125 \: {cm}^{3}$

$\purple{\bold{ \sf let \: the \: no. \: of \: cubes \: formed \: be \: \purple{'x'} }}$

$\implies \sf x = \frac{vol. \: of\: cuboid}{vol. \: of \: cube}$

$\implies \sf x = \frac{ \cancel{3750}}{ \cancel{125} }$

$\orange{ \therefore \sf x = 30 }$

$\therefore \sf 30 \: cubical \: blocks \: can \: be \: formed \: from \: solid \: \\ \sf metal \: block.$