Question

find the length of cubical box whose volume is the 512 cubic cm.​

Answer 1

Answer:

8cm

Step-by-step explanation:

Let the side of the cubical box is x.

Volume of cube =(side)^3

512cm^3=(x)^3

(8cm)^3=(x)^3

x=8cm

hope it helps

Answer 2

Given:

✰ Volume of cubical box = 512 cm³

To find:

✠ The length of the cubical box.

Solution:

Cube:

A cube is a rectangular solid whose each face is a square.

Here we are provided with the volume of a cubical box. The cubical box is in the shape of cube and its each face is a square. Using the formula of volume of cube, putting the values in the formula and then doing the required calculations, we will find the length of its one side or in other words the length of the cubical box.

Let's find out...✧

✭ Volume of a cube = a³ ✭

Here,

• a is the length of each side of a cubical box or the edge of cube that is the cubical box.

Putting the values in the formula, we have:

➤ 512 = a × a × a

➤ 512 = a³

Now, by prime factorization method, we have:

➤ 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = a³

➤ 8 × 8 × 8 = a³

➤ 8³ = a³

Now, cube on both sides get cancel, or we can solve it...as,

➤ a = ³√8³

Cube root and cube gets cancel, we have:

➤ a = 8 cm

∴ The length of the cubical box = 8 cm

More Formulae for cube:

• Total surface area of a cube = 6a² [ a is the length of each side of a cube or the edge of cube.

• Lateral surface area = 4a²

• Length of its diagonal = a√3

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