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Question

Three solid cubes have a face diagonal of 42 cm each. Three other solid cubes have a face diagonal of 82 cm each. All the cubes are melted together to form a cube. The side of the cube so formed is of length ___________.

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Solution

We know that each face of a cube is a square.

Let the side of solid cube having face diagonal of 42 cm each be x cm.

Diagonal of a square = 2×Side=2x

2x=42

⇒ x = 4 cm

Now, let the side of solid cube having face diagonal of 82 cm each be y cm.

2y=82

⇒ y = 8 cm

Suppose the side of the bigger cube obtained on melting the given cubes be a cm.

∴ Volume of the bigger cube = 3 × Volume of cube having side 4 cm + 3 × Volume of cube having side 8 cm

a3=3×43+3×83a3=192+1536=1728a3=123a=12 cm

Three solid cubes have a face diagonal of 42 cm each. Three other solid cubes have a face diagonal of 82 cm each. All the cubes are melted together to form a cube. The side of the cube so formed is of length __12 cm__.

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