Question

a solid cube of side 12cm is cut into 8 cubes of equal volume
What will be the side of the new cube? Also, Find the ratio between their surface are

Answer 1

$\boxed{\bold{\large{Answer:}}}$

$\text{Side\:of\:the\:solid\:cube\:(a)\:=\:12\:cm}$

$\text{Volume\:of\:the\:solid\:cube\:=\:a^3}$

$\implies \: (12 {)}^{3} = 12 \times 12 \times 12 \\ \\ = 1728c {m}^{3}$

$\text{It's\:cut\:into\:8\:pieces\:of\:equal\:volume.}$

$\text{Volume\:of\:a\:new\:cube}$

$= \frac{1728}{8} \: c {m}^{3} \\ \\ = 216 \: c {m}^{3}$

$\text{Let\:the\:side\:of\:the\:new\:cube\:be\:x\:cm}$

$\text{According\:to\:the\:Question}$

${x}^{3} = 216 \\ \\ \implies \: x = (216 {)}^{ \frac{1}{3} } \\ \\ \implies \: x \: = (6 \times 6 \times 6 {)}^{ \frac{1}{3} } \\ \\ \implies \: x \: = 6cm$

$\text{Thus,Side\:of\:the\:new\:cube\:is\:6cm}$

$\text{Surface\:area\:of\:the\:original\:cube}$

$= 6 {a}^{2} \\ \\ = 6(12 {)}^{2} \: c {m}^{2}$

$\text{Surface\:area\:of\:the\:new\:cube}$

$= 6 {x}^{2} = 6(6 {)}^{2} \: c {m}^{2}$

$\text{Thus\:Ratio\:between\:their\:surface\:areas}$

$= \frac{Surface \: Area \: Of \: The \: Original \: Cube \:}{Surface \: Area \: Of \: The \: New \: Cube } \\ \\ = \frac{6(12 {)}^{2} }{6(6 {)}^{2} } = \frac{4}{1} = 4:1$

$\text{Thus, The\:Ratio\:between\:their\:surface\: area\:is\:4\::\:1}$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

hope it's help u.............