Question

a solid cube of 12 cm is cut into 8 cubes of equal volume what will be the side of the new cube also find the ratio between their surface area​

Answer 1

Answer:

Original volume of cube - 12³ = 1728 cm³

This volume has been divided into eight.

So, volume of new cube = 1728/8 = 216 cm³

Since volume is a³, side will be a

³√216 = 6cm

Side of the new cube is 6cm

Surface area of original cube= 6a²=

6×12² = 6×144 = 864 cm²

Surface area of new cube - 6× 6²= 6×36 = 216 cm²

Their ratio is 864:216

== 4:1

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Answer 2

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

${\bold{\therefore Side\:of\:small\:cube=6\:cm}}$

${\bold{\therefore Ratio=1:4}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a solid cube of 12 cm is cut into 8 cubes of equal volume.

• We have to find the ratio of their surface area and side of small cube.

$\underline \bold{Given : } \\ \implies Side \: of \: big \: cube = 12 \: cm \\ \\ \underline \bold{To \: Find : } \\ \implies Side \: of \: small \: cube = ? \\ \\ \implies Ratio \: of \: T.S.A \: of \: small \: and \: big \: cube = ?$

• According to given question :

$\bold{Using \: formula \: volume \: of \: cube : } \\ \implies Volume \: of \: big \: cube = {( a_{1}})^{3} \\ \\ \implies Volume = ({12})^{3} \\ \\ \bold{\implies Volume = 1728 \: {cm}^{3} } \\ \\ \bold{For \: volume \: of \: small \: cube : } \\ \implies Volume \:o f \: small \: cube = \frac{1728}{8} \\ \\ \bold{\implies Volume = 216 \: {cm}^{2} } \\ \\ \bold{For \: sid e\: of \: small \: cube : } \\ \implies Volume \: of \: small \: cube = 216 \\ \\ \implies { a_{2} }^{3} = 216 \\ \\ \implies a_{2}= \sqrt{216} \\ \\ \bold{\implies a_{2} = 6 \: cm} \\ \\ \bold{Ror \: Ratio \: of \: T.S.A\: of \: small \: and \: big \: cube : } \\ \implies Ratio = \frac{T.S.A\: of \: small \: cube}{T.S.A \: of \: big \: cube} \\ \\ \implies Ratio = \frac{6 { a_{1} }^{2} }{6 { a_{2}}^{2} } \\ \\ \implies Ratio = \frac{( {6})^{2} }{ ({12})^{2} } \\ \\ \implies Ratio = \frac{ \cancel6 \times \cancel6}{ \cancel{12} \times \cancel{12}} \\ \\ \implies Ratio = \frac{1}{4} \\ \\ \implies \bold{Ratio = 1 : 4}$