Question

Example 5: Three metallic cubes of sides 4 cm, 3 cm,
and 5 cm are melted and recast into a new cube. Find
the edge of the new cube so formed.

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Answer 1

(3 metallic cubes) ⟶ (New cube)

3 metallic cubes of sides 4 cm, 3 cm, 5 cm.

Let the sides of cubes be (a₁), (a₂) and (a₃) respectively.

Volume of first cube = (a₁)³

⇒ Volume of first cube = 4³

∴ Volume of first cube = 64 cm³

Volume of second cube = (a₂)³

⇒ Volume of second cube = 3³

∴ Volume of second cube = 27 cm³

Volume of third cube = (a₃)³

⇒ Volume of third cube = 5³

∴ Volume of third cube = 125 cm³

These 3 cubes are melted and recast into a new cube

So, Volume of new cube = Sum of volumes of 3 cubes

Volume of new cube = 64 + 27 + 125 cm³

⇒ Volume of new cube = 216 cm²

Now let's find the edge of new cube so formed.

Volume of new cube = (Edge)³

→ 216 = (Edge)³

→ (Edge)³ = 216

→ Edge = ∛216

→ Edge = ± 6 cm

Side of cube cannot be negative.

∴ Edge = 6 cm