The surface area of a cuboid is 112 cm2. 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 cm3) of each cube?
Answers
- 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