Question

The length, breadth and height of 2 solid metal rods are 4 cm, 2 cm, 1 cm and 7 cm, 4 cm, 2 cm respectively. These are melted and combined to form a cube. What is the length of the cube?

Answer 1

We have,

The length, breadth and height of 2 solid metal rods are 4 cm, 2 cm, 1 cm and 7 cm, 4 cm, 2 cm respectively. These are melted and combined to form a cube.

Now we know that,

Volume of a cuboid = (Length) × (Breadth) × (Height)

Then, volume of first metal rod = (4)(2)(1) = 8 cm³

And the volume of the second metal rod = 742 = 56 cm³

Now, Volume of first metal rod + Volume of second metal rod = Volume of a cube

8 + 56 = (Edge)³

(Edge)³ = 64

(Edge)³ = 4 × 4 × 4

(Edge) = 4 cm

Therefore, the length of the cube is 4 cm.