Question

:. A solid cube of side 12 cm is cut into eight cubes of equal
volume. What will be the side of the new cube? Also find
the ratio between their surface areas.
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Answer 1

hope it will help you a lot .

Answer 2

$\large\boxed{\mathfrak{QuestioN:}}$

A solid cube of side 12 cm is cut into eight cubes of equal

volume. What will be the side of the new cube? Also find

the ratio between their surface areas.

$\large\boxed{\mathfrak{AnsweR:}}$

Here, cube of 12 cm is divided into 8 cubes of side a cm.

Given that :

Their volumes are equal.

Volume of big cube of side 12 cm=volume of 8 cubes of a cm,

(Side of big cube)^3=8*(side of small cube)^3,

(12)^3=8*a^3

(12*12*12)=8*a^3,

$\bold{\frac{1}{8}*12*12*12=a^3 }$.

$\bold{a^3=\frac{1}{8}*12*12*12, }$

$\bold{a^3=\frac{1}{2*2*2}*12*12*12, }$

$\bold{a^3=6*6*6\:cm^3}$,

$\bold{a^3=6^3\:cm^2}$.

a=6cm.

So, side of small cube is 6 cm.

Ratio of their surface area = $\bold{\frac{surface\:area\:of\:cube\:of\:side\:12\:cm}{surface\:area\:of\:cube\:of\:side\:6\:cm}}$

$\bold{\frac{6(side\:of\:big\:cube)^2}{6(side\:of\:small\:cube)^2} }\\\\\bold{\frac{6*12*12}{6*6*6}=\frac{4}{1}, }$

So the ratio of surface area is 4:1.

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