Question

8-The volume of a cubical box is 4096 cm. find the length of its edge.​

Answer 1

• The length of the edge of a cubical box = 16 cm.

Given :–

• The volume of a cubical box = $\sf 4096 \: {cm}^{3}.$

To Find :–

• The length of the edge (side) of a cubical box.

Solution :–

Given,

Volume of cube = $\sf 4096 \: {cm}^{3}$

Volume of cube = Side × Side × Side

$\mapsto {side}^{3} = 4096 \: {cm}^{3}$

$\mapsto side = \sqrt[3]{4096 \: {cm}^{3} }$

We know that,

• 16³ = 4096

So,

$\mapsto side = \sqrt[3]{16 \times 16 \times 16 \: {cm}^{3} }$

$\mapsto side = 16 \: cm$

Hence,

The length of the edge (side) of a cubical box is 16 cm.

Additional Information :–

Some formulas related to cube.

1) Volume of a cube = Side³.

2) Total surface area (T.S.A.) of a cube = 6 × Side².

3) Lateral surface area (L.S.A.) of a cube = 4 × Side².

4) Perimeter of a cube = 12 × Side.

5) Diagonal of a cube = √3 × Side.