Question

Three cubes whose edges measure 3cm, 4cm and 5cm respectively are melted
to form a new cube. Find T.S.A of the new cube.​

Answer 1

Given :-

• Edge of three cubes are 3 cm, 4 cm and 5 cm respectively.

To find :-

• T.S.A of new cube?

Solution :-

• Let side of cube₁ be = a₁
• Let side of cube₂ be = a₂
• Let side of cube₃ be = a₃
• And, side of new cube be = a

Three cubes are melted to form a new cube.

According to the Question:

Volume of cube₁ + Volume of cube₂ + Volume of cube₃ = Volume of new cube

We know that,

★ Volume of cube = a³

Therefore,

➻ (a₁) + (a₂) + (a₃) = a³

➻ (3)³ + (4)³ + (5)³ = a³

➻ 27 + 64 + 125 = a³

➻ 216 = a³

➻ a = 6 cm

∴ Side of new cube is 6 cm.

Now, Finding TSA of new cube,

We know that,

★ TSA of cube = 6a²

Putting value,

➻ 6 × 6²

➻ 216 cm²

∴ Hence, Total surface area of new cube is 216 cm²