Question

how many cubes of 5cm edges can be put in a cubical box of 1m edge​

Answer 1

Answer:

$\red\bigstar$ 8000 cubes of 5cm edges can be put in a cubical box of 1m edge​.

Small Cube

Side/Edge of the cube = 5cm.

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 5cm}\put(13.5,3){\bf\large 5cm}\put(-4,5.8){\bf\large 5cm}\end{picture}$

Volume of the cube = a³ , where a is the side of the cube.

⇒ Volume of the cube = 5³

⇒ Volume of the cube = 125 cm³.

Large Cube

Side / edge of the cube = 1m = 100cm.

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 100cm}\put(13.5,3){\bf\large 100cm}\put(-4,5.8){\bf\large 100cm}\end{picture}$

Volume of the cube = a³ , where a is the side of the cube.

⇒ Volume of the cube = 100³

⇒  Volume of the cube = 1000000cm³

$\boxed{\sf Number \: of \: cubes\: of \:edge\:5cm \:can \:be \:put\: in\: a \:cube\;of \: side \: 1m = \dfrac{Volume \; of \; the cube \; of \; edge \;100cm}{Volume \; of\: the \;cube \; of \;edge \;5cm} }$

$\implies \sf Number \: of \: cubes\: of \:edge\:5cm \:can \:be \:put\: in\: a \:cube\;of \: side \: 1m = \dfrac{1000000}{125}$

$\implies \sf Number \: of \: cubes\: of \:edge\:5cm \:can \:be \:put\: in\: a \:cube\;of \: side \: 1m = 8000$