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  • 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.

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.

Answers (1)

best_answer

If the side of cube=x

then Volume of the cube is given as V=x^3

In the question cube of the side, 12 cm is divided into 8 cubes of side a cm.
So using Initial Volume= Final volume
i.e 

The volume of big cube of side 12 cm= Volume of 8 cubes of side a cm
i.e (Side \ of \ big \ cube) $^{3}=8 \times\left(\text { Side of small cube) }^{3}\right.$
 
\begin{aligned} (12)^{3} &=8 \times a^{3} \\ \ \ \ \Rightarrow (12 \times 12 \times 12) &=8 \times a^{3} \\ \ \ \ \ \Rightarrow \frac{1}{8} \times 12 \times 12 \times 12 &=a^{3}\\ \Rightarrow \frac{12*12*12}{8}=a^3 \end{aligned}

i.e

 a^3=\frac{12*12*12}{8}=\frac{12*12*12}{2*2*2}\\\Rightarrow a=\frac{12}{2}=6

i.e  Side of small cube =6 cm

Posted by

avinash.dongre

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