8 equal cube is cut out form a cuboid of dimension 4 cm × 2 cm × 1 c

1.	8 equal cube is cut out form a cuboid of dimension 4 cm × 2 cm × 1 cm. What is the ratio of the total surface area of the cuboid to that of all 8 cubes?1. 7 : 182. 5 : 113. 9 : 134. 7 : 12
Answer» Correct Answer - Option 4 : 7 : 12 Given: Dimension of cuboid = 4 cm × 2 cm × 1 cm Formula: Volume of cuboid = lbh Total surface are of cuboid = 2 (lb + bh + hl) Volume of cube = a³ Total surface area of cube = 6a² Calculation: Volume of cuboid = 4 × 2 × 1 = 8 cm³ Volume of each cube = 8 / 8 = 1 cm³ Side of each cube = ∛1 = 1 cm Total surface area of cuboid = 2 (4 × 2 + 2 × 1 + 1 × 4) ⇒ 2 × (8 + 2 + 4) ⇒ 2 × 14 ⇒ 28 cm² Total surface area of all 8 cubes = 8 × 6 × 1² ⇒ 48 cm² ∴ Required ratio = 28 : 48 = 7 : 12

8 equal cube is cut out form a cuboid of dimension 4 cm × 2 cm × 1 cm. What is the ratio of the total surface area of the cuboid to that of all 8 cubes?1. 7 : 182. 5 : 113. 9 : 134. 7 : 12

Answer» Correct Answer - Option 4 : 7 : 12

Given:

Dimension of cuboid = 4 cm × 2 cm × 1 cm

Formula:

Volume of cuboid = lbh

Total surface are of cuboid = 2 (lb + bh + hl)

Volume of cube = a³

Total surface area of cube = 6a²

Calculation:

Volume of cuboid = 4 × 2 × 1 = 8 cm³

Volume of each cube = 8 / 8 = 1 cm³

Side of each cube = ∛1 = 1 cm

Total surface area of cuboid = 2 (4 × 2 + 2 × 1 + 1 × 4)

⇒ 2 × (8 + 2 + 4)

⇒ 2 × 14

⇒ 28 cm²

Total surface area of all 8 cubes = 8 × 6 × 1²

⇒ 48 cm²

∴ Required ratio = 28 : 48 = 7 : 12

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