Question

The surface area of
a cuboid is 112 cm?
Its length is twice its
breadth and its
height is half its
breadth. If it is
melted to form 2
identical cubes
without any wastage,
what is the volume
(in cm) of each
cube?​

Answer 1

• First Let's Find Surface Area of Cuboid

Surface Area of Cuboid = 2 (lb + bh + lh)

⇒ Surface Area of Cuboid = 2 [(l × b) + (b × h) + (l × h)]

⇒ Surface Area of Cuboid = 2 [(2b × b) + (b × 1/2 b) + (2b × 1/2 b)]

⇒ Surface Area of Cuboid = 2 [(2b²) + (b²/2) + (2b²/2)]

⇒ Surface Area of Cuboid = 2 [2b² + (b²/2) + b²]

⇒ Surface Area of Cuboid = 2 [3b² + (b²/2)]

⇒ Surface Area of Cuboid = 6b² + b²

⇒ Surface Area of Cuboid = 7b² cm²

Substituting the value of Surface Area of Cuboid

⇒ 112 cm² = 7b² cm²

⇒ 112 = 7b²

⇒ 112/7 = b²

⇒ 16 = b²

⇒ √16 = √b²

⇒ 4 = b

⇒ b = 4

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Volume of 2 Cubes = Length × Breadth × Height

⇒ Volume of 2 Cubes = 2b × b × 1/2 b

⇒ Volume of 2 Cubes = 2b² × 1/2 b

⇒ Volume of 2 Cubes = b² × 1b

⇒ Volume of 2 Cubes = b³

Substitute the Value of b

⇒ Volume of 2 Cubes = 4³

⇒ Volume of 2 Cubes = 64 cm³

⇒ Volume of  Cube = 64 cm³/2

⇒ Volume of  Cube = 32 cm³