Question

A cube is cut into smaller cubes such that each side of the smaller cubes is half of other cube. the total surface area is increased by : a) 100% b)200% c)300% d)400%

Answer 1

Answer:

if a cube is cut into smaller cubes

let the cube be x

the smaller cube be x/2

the area of large cube =6a²

the area of small cube =6/2a²=3a²

the total percent = 6a²/3a²*100 = 200%

Answer 2

Answer:

Option a) 100% is correct .

Step-by-step explanation:

Let the side of bigger cube be x and side of smaller cube is y.

Surface area of bigger cube is $6x^{2}$.

Each side of smaller cube is half of bigger cube. y= x/2

Surface area of smaller cube = $6y^{2}$ =  $6x^{2} /4$ = $3x^{2} /2$

Total surface area of smaller cube = 8× $3x^{2} /2$

                                                         = $12x^{2}$

Percentage increase in total surface area = $( 12x^{2} - 6x^{2} )$ × $100$ / ( $6x^{2}$)

                                                                      =$100%$%

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