How surface area varies?

Geometry Level 2

A cube of 1 cm side length is cut into 1000 (identical) cubes of 1 mm side length. Now find the ratio of Surface Area of these 1000 cubes to that of the original cube.

1:10

100:1

10:1

1:100

1:1000

1000:1

1 solution

Charley Shi
Apr 12, 2021

A cube has 6 faces so a cube with side length $x$ has surface area $A_s = 6x^2$ Thus, for the 1cm cube: $A_{s1} = 6(1cm)^2 = 6cm^2$ The total surface area of the 1000 1mm cubes: $A_{s2} = 1000\times 6(0.1cm)^2 = 1000\times6\times 0.01cm^2 = 60cm^2$ $A_{s2} = 10A_{s1}$ so the answer is $\boxed{10:1}$ .

How surface area varies?

1 solution

0 pending reports