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A cube of side 6 cm is painted with blue colour and cut into small cubes of side 1 cm, the small cubes which has no painted side is painted with red colour. And the remaining areas of remaining small cubes are painted with green colour. Find the ratio of blue painted, red painted and green painted area.

A cube of side 6 cm is painted with blue colour and cut into small cubes of side 1 cm, the small cubes which has no painted side is painted with red colour. And the remaining areas of remaining small cubes are painted with green colour. Find the ratio of blue painted, red painted and green painted area. Correct Answer 27 ∶ 48 ∶ 87

Area which is painted with blue colour = 6 × 6 × 6 = 216 cm3

When the cube is cut into cubes of side 1 cm,

⇒ Number of cubes with only one side painted with blue colour = 6 × 4 × 4 = 96

⇒ Number of cubes with only two sides painted with blue colour = 12 × 4 = 48

⇒ Number of cubes with only three sides painted with blue colour = 8

⇒ Number of cubes with only no side painted with blue colour = 216 - 96 - 48 - 8 = 64

⇒ Area which is painted with green colour = 96 × 1 × 5 + 48 × 1 × 4 + 8 × 1 × 3 = 480 + 192 + 24 = 696

⇒ Area which is painted with red colour = 64 × 1 × 6 = 384

∴ Ratio of blue painted, red painted and green painted area = 216 ∶ 384 ∶ 696 = 27 ∶ 48 ∶ 87

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