A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is mel

1.	A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes? 1. 2 : 32. 7 : 123. 4 : 74. 7 : 8
Answer» Correct Answer - Option 4 : 7 : 8 Given: A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm where l = 18 cm, b = 36 cm and h = 72 cm It is melted and recast into 8 cubes of the same volume. Concept used: The volume of cuboid = lbh The total surface area of the cuboid = 2(lb + bh + hl) Where l = length, b = breadth and h = height The volume of cube = a³ The lateral surface area of cube = 4 × a² Where a = side of cube Explanation: according to the question, lbh = 8 × a³ ⇒ 18 × 36 × 72 = 8 × a³ ⇒ a³ = 18 × 36 × 9 ⇒ a = √(9 × 2 × 9 × 2 × 2 × 9) ⇒ a = 18 cm now, according to the question, 2(lb + bh + hl) : 8 × 4 × a² ⇒ 2(18 × 36 + 36 × 72 + 72 × 18) : 8 × 4 × (18)² ⇒ 2 × 18 × 36(1 + 4 + 2) : 8 × 4 × 18 × 18 ⇒ 36 × 36 × 7 : 32 × 18 × 18 ⇒ 7 : 8 ∴ The ratio is 7 : 8.

A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes? 1. 2 : 32. 7 : 123. 4 : 74. 7 : 8

Answer» Correct Answer - Option 4 : 7 : 8

Given:

A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm

where l = 18 cm, b = 36 cm and h = 72 cm

It is melted and recast into 8 cubes of the same volume.

Concept used:

The volume of cuboid = lbh

The total surface area of the cuboid = 2(lb + bh + hl)

Where l = length, b = breadth and h = height

The volume of cube = a³

The lateral surface area of cube = 4 × a²

Where a = side of cube

Explanation:

according to the question,

lbh = 8 × a³

⇒ 18 × 36 × 72 = 8 × a³

⇒ a³ = 18 × 36 × 9

⇒ a = √(9 × 2 × 9 × 2 × 2 × 9)

⇒ a = 18 cm

now,

according to the question,

2(lb + bh + hl) : 8 × 4 × a²

⇒ 2(18 × 36 + 36 × 72 + 72 × 18) : 8 × 4 × (18)²

⇒ 2 × 18 × 36(1 + 4 + 2) : 8 × 4 × 18 × 18

⇒ 36 × 36 × 7 : 32 × 18 × 18

⇒ 7 : 8

∴ The ratio is 7 : 8.