Question

A cube of side 60m can accommodate some smaller cubes of side 2m .How many small cubes can be placed in the given cube?

Answer 1

Given:

• A cube of side 60m can accommodate some smaller cubes of side 2m

To Find:

• How many small cubes can be placed in the given cube?

Understanding the concept:

So here it is given that, A cube of the edge 60m can accommodate. Which means that the smaller cubes of side 2m are to be fit in volume of the larger cube of side 6m so, that means volume of the bigger cube equals total volume of the smaller cubes.

Solution:

Now let's find the volume of the big cube,

As we know that,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \star { \underline{ \boxed{ \frak{ volume \: of \: a \: cube = {side}^{2} }}}}$

Substituting the values we get,

$\longrightarrow \tt \: \: volume = {side}^{3} \: \: \\ \\ \\ \longrightarrow \tt \: \: volume = {6}^{3} \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: \: volume = 216 {m}^{3} \:$

${ \underline{ \pmb{ \frak{ hence \: the \: volume \: of \: the \: big \: cube \: is \: { \pink{216 {m}^{3} }}}}}}$

Now let's find the volume of the smaller cube,

• Substituting the values we get,

$\longrightarrow \tt \: \: volume = {side}^{3} \\ \\ \\ \longrightarrow \tt \: \: volume = {2}^{3} \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: \: volume = {8m}^{3} \: \:$

${ \underline{ \pmb{ \frak{ hence \: the \: volume \: of \: the \: big \: cube \: is \: { \pink{8 {m}^{3} }}}}}}$

Now,

$\purple \mapsto \tt \: no.of \: cubes \: which \: can \: fit = \frac{volume \: of \: big \: cube}{volume \: of \: small \: cube} \\ \\ \\ \purple \mapsto \tt \: no.of \: cubes \: which \: can \: fit = \cancel\frac{216}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \purple \mapsto \tt \: no.of \: cubes \: which \: can \: fit = \pink{ \boxed{ \tt{27 \bigstar}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore,

• The big cube can accomodate 27 number of small cubes

More to know,

• Volume of a cubiod = l × b × h
• Total surface area of a cubiod = 2(hl+lb+bh)
• Total surface area of a cube = 4(side)²
• Curved surface area of the cylinder = 2πrh
• Total surface area of a cylinder 2πrh + 2πr2
• Volume of a cylinder is πr²h