Question

Three cubes having edges 18 cm, 24 cm and 30 cm respectively are melted and made into a new cube.find
the edge of the new cube so formed.
​

Answer 1

$\bigstar \underline{\underline{\sf \bf Given:-}}$

• Edges of three cubes = 18cm,24cm&30cm.
• They are melted and made into a new cube.

$\bigstar \underline{\underline{\sf \bf To\ find:-}}$

• The edge of new cube.

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

We know :

❥ Volume of a cube = a³.

Where , a = edge.

Now,

→ Volume of first cube

⇒ 18 ³ = 5832

→ Volume of second cube ,

⇒ 24³ = 13824 .

→ Volume of third cube ,

⇒ 30³ = 27000.

→ Total vol. of all cubes = 5832 + 1384 + 27000

                                       = 46656 cm³.

According to question :

❥ Vol of new cube = Total vol of three cubes.

=> Vol of new cube (a³) = 46656

⇒ a = ∛46656

⇒ a = 36cm.

Hence, Edge of new cube formed is 36cm.

_____________________

Answer 2

$\bigstar\huge\bf\underline{\underline{\blue{Answer:-}}}$

The edge of the new cube = 36 cm

$\bigstar\bf\underline\red{Given:-}$

• Firstly take the three edges as A, B, C

• Edge of cube A = 18 cm

• Edge of cube B = 24 cm

• Edge of cube C = 30 cm

$\bigstar\bf\underline\green{To \ find:-}$

• The edge of new cube

$\arrow$ $\bigstar\bf\underline\orange{Solution:-}$

→"Volume of cube = a³"

and, a = edge

Now,

Volume of cube A

⇒V₁ = (18)³

⇒5832cm³

Volume of cube B

⇒V₂ = (24)³

⇒13824cm³

Volume of cube C

⇒V₃ = (30)³

⇒27000cm³

Total volume of cube A, B, C

⇒(5832 + 13824 + 27000)cm³

⇒46656cm³

Let a be the edge of new cube

∴Volume = a³ = 46656

a = ∛46656

⇒∛6 × 6 × 6 × 6 × 6 × 6

⇒6 × 6

⇒36cm³

Therefore, the volume of  edge of the new cube is "36cm³