Question

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

Answer 1

$\fbox{\fbox{\large{\purple{\mathfrak{Answer:-}}}}}$

The surface of area after such cutting is 400%

$\fbox{\fbox{\red{\large{\mathfrak{Solution:-}}}}}$

$surface \: area \: of \: 5cm \: cube \: \\ = 6 \times ( {5cm)}^{2} = {150cm}^{2}$

$volume \: of \: cube \: of \: \: 5cm = n \times \\ (volume \: of \: cube \: 1cm)$

$5 \times 5 \times 5 =n \times (1 \times 1 \times 1)$

$25 = n \times (1)$

$n = 25$

When it cut into 1 cm cubes, then there will be 125 cubes which have side 1 cm.

Surface area of 1 cm side cube

$= 6 \times ( {1)}^{2} = 6 {cm}^{2}$

Surface area of 125 cubes of side

$1cm = 125 \times 6 = 75 {0cm}^{2}$

Thus percentage increase

$= ( \frac{final \: area - intial \: area}{intial \: area \: } ) \times 100 \\ = \frac{600}{150} \times 100 = 400\%$

Answer 2

Earlier surface area of the cube = 6(side)^2

= 6(4)^2

= 96cm^2

No. of new cubes = Volume of older cube / Volume of 1 new cube

=> 4*4*4/1*1*1

=> 64 cubes

Newer surface area of 64 cubes = 64*6(1)^2

= 384cm^2

Therefore, percentage increase => (384-96)*100/96

=> 28800/96

= 300%