Question

A solid cube of side 12 cm is cut into eight cubes of equal volume. Find the ratio between their surface areas.

• A. 3:1
• B. 4:1
• C. 5:1
• D. 6:1

Answer 1

The correct option is B 4:1

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.