Question

Three cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. Find its edge. Also, find the surface area of the new cube.​

Answer 1

Given:-

• Edge of 1st Cube = 3cm

• Edge of 2nd Cube = 4cm

• Edge of third Cube = 5cm

To Find:-

• The Edge of new cube formed and surface area of new cube.

Formulae used:-

• Volume of Cube = ( Side )³

• Surface area of Cube = 4a²

Where,

• a = Side

How to Solve ?

• First we will find the volume of each cube and will add it to get the volume of new cube.

• We can from there will find out the edge of new cube.

Now,

→ Volume of 1st Cube ( x ) = (side)³ → (3)³ = 27cm³

→ Volume of 2nd Cube ( y ) = (side)³ → (4)³ = 64cm³

→ Volume of 3rd Cube (z) = (side)³ → (5)³ = 125cm³

→ Volume of new cube = x + y + z → 27 + 64 + 125 → 216cm³

Therefore,

→ Edge of new cube formed = ³√216

→ Edge of new cube formed = 6cm.

Now,

→ Surface area of new cube = 4a²

→ Surface area of new cube = 4(6)²

→ 4 × 36

→ 144cm².

Hence, The Surface area of cube is 144cm².

Answer 2

Given : Three cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube.

　

To find : what is its edge, what is the surface area of the new cube.

　

Solution :

→ 3³ + 4³ + 5³

→ 27 + 64 + 125

→ 216 cm³

　

→ 6 cm

　

→ 6 × 6² (6 a²)

→ 216 cm³

　

Therefore,

1. Edge of new cube = 6 cm.
2. Surface area of new cube = 216 cm².