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.

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#### Solution

Side (*a*) of cube = 12 cm

Volume of cube = (*a*)^{3} = (12 cm)^{3} = 1728 cm^{3}

Let the side of the smaller cube be *a*_{1}.

`"Volume of 1 smaller cube "=(1728/8)cm^3=216cm^3`

(a_{1})^{3} = 216 cm^{3}

⇒ *a*_{1} = 6 cm

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

`"Ratio between surface areas of cubes "="Surface area of bigger cube"/"Surface area of smaller cube"`

`=(6a^2)/(6a_1^2) = 12^2/6^2 = 4/1`

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

Concept: Volume of a Cuboid

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