Question

Solid cube of sides 12 cm is cut into eight cube of equal volume. What will be the sides of the new cube? Find the ratio between their surface area.

Answer 1

Step-by-step explanation:

Volume of the cube is, V1 = (12)^3 = 1728 cm^3

Volume of the each one of the 8 cubes will be, V2 = 1728/8 = 216 cm^3

Sides of the new cube will be, l =

$\sqrt[3]{216}$

l = 6 cm

Now for ratio between their SA, we have :

r = A1/A2 = {6*(8*8)} / {6*(6*6)}

r = 16/9

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• Cube of sides 12 cm

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• Cube is cut into eight cube of equal volume

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$\red{\underline \bold{To \: Find:}}$

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• Sides of the new cube

$\:\:$

• Ratio between their surface area.

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Volume of the solid cube = $\rm a^3$

$\:\:$

$\underline{\bold{\texttt{Volume of cube :}}}$

$\:\:$

$\sf \longmapsto (12)^3 = 12 x 12 x 12$

$\:\:$

$\bf \dag \: \: 1728 \: cube \: cm$

$\:\:$

It is cut into eight cubes of equal volume.

$\:\:$

$\underline{\bold{\texttt{Volume of a new cube}}}$

$\:\:$

$\sf \longmapsto \dfrac { 1728 } { 8 }$

$\:\:$

$\bf \dag \: \: 216 \: cube \: cm$

$\:\:$

Let the side of the new cube be x cm.

$\:\:$

Then, volume of the new cube = $\rm x^3 \: cm$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\rm \longmapsto x^3 = 216$

$\:\:$

$\sf \longmapsto x = (216)^{\frac { 1 } { 3 } }$

$\:\:$

$\sf \longmapsto x = (6 x6 x 6)^{\frac { 1 } { 3 }}$

$\:\:$

$\bf \dashrightarrow x = 6 \: cm$

$\:\:$

Hence, the side of the new cube will be 6 cm.

$\:\:$

$\underline{\bold{\texttt{Surface area of the original cube :}}}$

$\:\:$

$\rm \dag \: \: \: \: 6a^2$

$\:\:$

$\rm \longmapsto 6(12)^2 \: cm^2$

$\:\:$

$\underline{\bold{\texttt{Surface area of the new cube :}}}$

$\:\:$

$\rm \dag \: \: \: \: 6x^2$

$\:\:$

$\rm \longmapsto 6(6)^2 \: cm^2$

$\:\:$

$\underline{\bold{\texttt{Ratio between their surface areas}}}$

$\:\:$

$\sf \longmapsto \dfrac { Surface \: area \: of \: original \: cube } { Surface \: area \: of \: new \: cube }$

$\:\:$

$\sf \longmapsto \dfrac { 6(12)^2 } { 6(6)^2 }$

$\:\:$

$\sf \dashrightarrow \dfrac { 4 } { 1 }$

$\:\:$

$\bf \dag \: \: 4 : 1$

$\:\:$

Side of new cube is 6 cm

Hence the ratio is 4 : 1

$\rule{200}5$