Question

Question 8
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

Side(a) of the cube = 12 cm

Volume of the cube $=(a{)}^3=(12cm{)}^3=1728c{m}^3$

Let the side of the smaller cube be $a_1$.

Volume of 1 smaller cube $=\left(\frac{1728}{8}\right)c{m}^3=216c{m}^3(a_1{)}^3=216c{m}^3\Rightarrow a_1=6cm$

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes $=\frac{Surfaceareaofbiggercube}{SurfaceareaofSmallercube}=\frac{6\times {12}^2}{6\times 6^2}=\frac{(12{)}^2}{(6{)}^2}=\frac{4}{1}$

Therefore, the ratio between the surface areas of these cubes is 4:1.