Question

How much area (in sq.units) will a cube of volume a² cubic units cover on the floor

Answer 1

Solution :-

Given that

Volume of a cube = a² cubic units

We know that

Volume of a cube = side³ cubic units

Therefore, side ³ = a²

=> side = ³√a² units

=> side = (a²)⅓

=> side = a⅔ units

Therefore, Side of the cube = a⅔ units

We know that

Each floor of the cube is a square shape

Area of the each floor of the cube = side² sq.units

Area of the floor of the cube = (a⅔)² sq.units

=> a(²×⅔)

=> a⁴/³ or ³√a⁴ sq.units

Answer :-

The area of the floor of the cube is a⁴/³ sq.units (or) ³√a⁴ sq.units

Points to know :-

The edge of a cube is 'a' units then

→ A cube has 6 faces ( floors)

→ Area of a each edge = a² sq.units

→ Lateral Surface Area = 4a² sq.units

→ Total Surface Area = 6a² sq.units

→ Volume = a³ cubic units

→ Length of the diagonal = √3 a units

Answer 2

Answer:

$\sqrt{3a \: units}$

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