Question

A 5 cm cube is cut into 1 cm cubes. The percentage increase in the surface area after such cutting is

• A. 100%
• B. 200%
• C. 300%
• D. 400%

Answer 1

The correct option is D

400%

Surface area of 5 cm cube $=6\times (5cm{)}^2=150c{m}^2$
Volume of cube of $5cm=n\times$ (volume of cubes of 1cm)
$5\times 5\times 5=n\times (1\times 1\times 1)$
$25=n\times \left(1\right)$
$n=125$
When it is cut into 1 cm cubes, then there will be 125 cubes which have side of 1cm.
Surface area of 1 cm side cube $=6\times (1{)}^2=6c{m}^2$
Surface area of 125 cubes of side $1cm=125\times 6=750c{m}^2$
Thus percentage increase $=\left(\frac{FinalArea-InitialArea}{InitialArea}\right)\times 100=\frac{750-150}{150}\times 100=\frac{600}{150}\times 100=400\%$