Question

a cube of side 5cm cut into as many 1cm cube as possible .what is the ratio of surface area of original cube to that of sum of surface area of smaller cubes

Answer 1

surface area of cube is 4a^2
csa of original cube is 4×5^2=100
csa of smaller cube is4×1^2=4
so ratio is100:4=25:1

Answer 2

Divide the volume of Big cube by the volume of smaller cubes to get how many smaller cubes are cut from the bigger one.

then,

SA(for Big Cube) = 6a² = 6*5*5 = 150cm²
SA(for 125 small Cubes) = 6a² = 6*1*1*125 = 750cm²

Ratio = SA(for Big Cube)/SA(for 125 small Cubes)
=150/750 = 1/4
∴, the ratio is 1:4.

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