Question

A surface of a cube are coloured . If a number of smaller cubes are taken out from it each side 1/4 is the size of the origional cubes side , indicate the number of cubes with only one side painted​

Answer 1

side of each of the new cube = 6 cm

Ratio between TSA of original cube and TSA of all the new cubes formed = 1 : 2

Step-by-step explanation:

The total volume of the 8 cubes will be equal to the volume of the original cube.

Let the side of the new cubes be S.

Hence,

8 × S^3 = 12^3

S^3 = 12^3 / 8

S^3 = (12 / 2)^3

S^3= 6^3

S = 6 cm

Since surface area of a cube = 6 × (side)^2,

Surface area of each of the new cube = 6 × (6)^2 = 6 × 36 = 216 cm^2

Hence, surface area of all the cubes :

8 × 216 = 1728 cm^2

Surface area of the original cube :

6 × (12)^2 = 6 × 144 = 864 cm^2

Hence,

Ratio = 864 : 1728 = 1 : 2