Question

6. How many small cubes of edge 10 cm can be put in a cubical box of side 80 cm?
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Answer 1

$\\ \\ \underbrace { \large\underline{ \sf \: Question :-}}$

How many small cubes of edge 10 cm can be put in a cubical box of side 80 cm?

$\\ \\ \underbrace { \large\underline{ \sf \: Answer :-}}$

$\\ \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: 512 \: small \: cubes \:$

$\\ \\ \underbrace { \large\underline{ \sf \: Explanation :-}}$

$\\ \\ \sf \: At \: first, \: we \: have \: to \: find \: the \: volume \: of \: the \: box , \\ \sf So \: let's \: start \: ,$

$\\ \\ \sf \: \: \: \: \: Volume \: of \: box \: = \: side ^{3}$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 80 ^{3}$

$\\ \\ \sf \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\boxed{ \orange{\tt Volume \: of \: box \: = \: 512000 \: {cm}^{3} }}}$

$\\ \\ \sf \: Now, \: We \: have \: to \: find \: the \: volume \: of \: one \: small \: cube$

$\\ \\ \sf \: \: \: \: \: Volume \: of \: one \: small \: cube \: = \: side ^{3}$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 10 ^{3}$

$\\ \\ \sf \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\boxed{ \orange{\tt Volume \: of \: one \: small \: cube \: \: = \: 1000 \: cm ^{3} }}}$

$\\ \sf \: So,$

$\\ \\ \sf \: \: \: In \: the \: box \: small \: cubes \: can \: fit$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \frac {Volume \: of \: box } {Volume \: of \: one \: small \: cube}$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: : \implies \: \frac{512000}{1000}$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: : \implies \: 512$

$\\ \\ \sf \therefore \: \: \underline{ \: Hence, \: 512 \: cubes \: can \: be \: fit \: in \: the \: box } \\ \\ \:$

Answer 2

$\underline{\boxed{\bold{ \bigstar \; Question \; \bigstar }}}$ $\; \; \; \;$

How many small cubes of edge 10 cm can be put in a cubical box of side 80 cm?

$\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}$ $\; \; \; \;$ ​

Volume of a cube = a³ --(where a = side of the cube)

∴ volume of the small cubes = (10)³

                                               = 1000 cm³

Volume of cube = a³ --(where a = side of the cube)

∴ volume of the cubical box = (80)³

                                               = 512000 cm³

Now, in order to find how many small cubes can manage to fit in the cubical box, we'll have to divide the volume of the box by volume of the cubes.

∴ $\frac{Volume of cubical box}{Volume of small cubes}$

= $\frac{512000}{1000}$

= 512

∴ 512 small cubes of 10 cm can fit in a cubical box of 80 cm.

Hope this helps uh! ♡