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A solid metallic cuboid of dimensions 12 cm × 9 cm × 16 cm is melted and recast into 216 cubes of the same size. What is the lateral surface area of two such cubes?

A solid metallic cuboid of dimensions 12 cm × 9 cm × 16 cm is melted and recast into 216 cubes of the same size. What is the lateral surface area of two such cubes? Correct Answer 32 cm<sup>2</sup>

Given:

Dimension of cuboid = 12 cm × 9 cm × 16 cm

Number of cubes = 216

Formula Used:

The volume of cuboid = Length × Breadth × Height

The volume of cube = (Side)3

The lateral surface area of cube = 4 × (Side)2

Calculation:     

The volume of cuboid = Length × Breadth × Height   

⇒ The volume of cuboid = 12 cm × 9 cm × 16 cm

⇒ The volume of cuboid = 1728 cm3

The volume of cuboid = 216 × The volume of cube

⇒ 1728 = 216 × (Side)3

⇒ 8 = (Side)3

⇒ Side = 2 cm

The lateral surface area of 2 cubes = 2 × 4 × (Side)2

⇒ The lateral srface area of 2 cubes = 8 × (2)2

⇒ The lateral surface area of 2 cubes = 32 cm2

∴ The lateral surface area of 2 cubes is 32 cm2 

The correct option is 2 i.e. 32 cm2

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