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.​

Answer 1

Let's consider side of new cube be a cm.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Solid cube of side 12 cm is divided into 8 cubes of equal volume.

⠀⠀⠀

Therefore,

$:\implies\sf Volume\:of\:big\:cube = 8 \times Volume\:of\:small\:cube$

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

⋆ Volume of cube is given by,

$\star\;{\boxed{\sf{\purple{Volume_{\;(cube)} = (side)^3}}}}$

$\sf Here \begin{cases} & \sf{Side\:of\:big\:cube = \bf{12\:cm}} \\ & \sf{Side\:of\:small\:cube = \bf{a\:cm}} \end{cases}$

$\dag\;{\underline{\frak{Now,\:Putting\:values,}}}$

$:\implies\sf (12)^3 = 8 \times (a)^3\\ \\ \\ :\implies\sf 12 \times 12 \times 12 = 8 \times (a)^3\\ \\ \\ :\implies\sf \dfrac{1}{ \cancel{8}} \times \cancel{12} \times 12 \times 12 = a^3\\ \\ \\ :\implies\sf \dfrac{1}{\cancel{4}} \times 6 \times \cancel{12} \times 12 = a^3\\ \\ \\ :\implies\sf \dfrac{1}{ \cancel{2}} \times 6 \times 6 \times \cancel{12} = a^3\\ \\ \\ :\implies\sf 6\times 6 \times 6 = a^3\\ \\ \\ :\implies\sf a^3 = (6)^3\\ \\ \\ :\implies\sf \sqrt[3]{a^3} = \sqrt[3]{6^3}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{a = 6}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Side\:of\:small\:or\:new\:cubes\:is\: {\textbf{\textsf{6\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{Finding\:ratio\:of\:their\:surface\:areas,}}}$

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

⋆ Surface area of cube is given by,

$\star\;{\boxed{\sf{\red{TSA_{\;(cube)} = 6 \times (side)^2}}}}$

Therefore,

$:\implies\sf \dfrac{Surface\:area_{\:(big\:cube)}}{Surface\:area_{\:(small\:cube)}}\\ \\ \\ :\implies\sf \dfrac{6 \times (12)^2}{6 \times (6)^2}\\ \\ \\ :\implies\sf \dfrac{\cancel{6 \times 12 \times 12}}{\cancel{6 \times 6 \times 6}}\\ \\ \\ :\implies\sf \dfrac{4}{1}\\ \\ \\ :\implies{\underline{\boxed{\frak{\green{4:1}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Thus,\:the\:ratio\:their\:surface\:area\:is\: {\textbf{\textsf{4:1}}}.}}}$

Answer 2

Answer:

4:1

Step-by-step explanation:

Volume of old cube =a³

⇒(12)³=1728 cm³

No.of cubes =8

Volume of old cube = 8* volume of 1 new cube

1728=8*a³

1728/8=a³

12/2=a

6 cm=a

Surface area of old cube/ surface area of new cube=6*(12)²/6*(6)²

=144/36=4/1=4:1

I hope it helps...

Stay Brainly...