Question

The dimensions of the a metallic cuboidal box are 100cm × 80cm × 64 cm . It is melted and recast into a cube . Find the surface area of the cube​

Answer 1

Answer:

38400 cm² is the required surface area of cube .

Step-by-step explanation:

According to the Question

It is given that the dimensions of Cuboidal box are 100cm×80cm×64cm . It is melted and recast into a cube .

we have to calculate the surface area of the resultant cube . Since , here the cuboidal box melted so , we calculate the volume of the box.

• Volume of box = l×b×h

Substitute the value we get

➻ Volume of box = 100×80×64

➻Volume of box = 8000 × 64

➻ Volume of box = 512000 cm³.

The metallic box is melted and recasted into a cube . So , the volume is constant here.

➻ Volume of box = volume of cube

➻ 512000 = a³

➻ 80 = a

➻ a = 80cm

Now, calculating the surface area of the resultant cube .

• Surface area of cube = 6a²

Substitute the value we get

➻ Surface area of cube = 6×80²

➻ Surface area of cube = 6×6400

➻ Surface area of cube = 38400 cm²

• Hence, the surface area of the cube is 38400cm².

Answer 2

Answer:

Volume = 100*80*64

Volume = 512000

Let length of cube be a

a³= 512000

a = 80

Surface area = 6*80*80

Surface area = 38400 cm²

So, the surface area of cube = 38400 cm².