Question

pls answer 13 :1st answer 16 cm 2nd answer 4096 cm3 3rd answer 721 cm3​

Answer 1

1. The length of the edge of a cube = 16 cm.
2. The volume of the cube = 4096 cm³.
3. The volume its material whose thickness is 5 mm = 768 cm³.

Given :

• The surface area of the cube = 1536 cm².

To Find :

1. The length of its edge.
2. The volume of the cube.
3. The volume of its material whose thickness is 5 mm.

Solution :

1) The length of its edge.

Given,

The surface area if the cube is 1536 cm²

We know that,

$\underline{ \boxed{ \bf{ \orange{Surface \: area \: of \: cube = {6a}^{2}} }}}$

Where,

• a = side.

$: \implies \bf 1536 \: {cm}^{2} = 6 \times {a}^{2} \\ \\ \\ : \implies \bf \dfrac{1536}{6} \: {cm}^{2} = {a}^{2} \\ \\ \\ : \implies \bf 256 \: {cm}^{2} = {a}^{2} \\ \\ \\ : \implies \bf \sqrt{256 \: {cm}^{2} } = a \\ \\ \\ : \implies \bf 16 \: cm = a \\ \\ \\ \: \: \bf \therefore \: \: a = 16 \: cm$

Hence,

The length of its edge is 16 cm.

______________________________

2) The volume of the cube.

We know that,

$\underline{ \boxed{ \orange{ \bf{Volume \: of \: cube = {a}^{3} }}}}$

Where,

• a = 16 cm [ Found above ]

Now, substitute the value of a in the formula of the volume of the cube.

$: \implies \bf {(16 \: cm)}^{3} \\ \\ \\ : \implies \bf 16 \: cm \times 16 \: cm \times 16 \: cm \\ \\ \\ : \implies \bf 4096 \: {cm}^{3} \\ \\ \\ \: \: \bf \therefore \: \: Volume \: Of \: Cube = 4096 \: {cm}^{3}$

Hence,

The volume of the cube is 4096 cm³.

______________________________

3) The volume of its material whose thickness is 5 mm.

$\underline{\boxed{\orange{\bf{Volume \: of \: material = Surface \: area \times Thickness}}}}$

Where,

• Surface area = 1536 cm².
• Thickness = 5 mm.

Since, the surface area is in cm and the thickness is in mm so, we need to change the mm into cm.

For changing mm to cm. We have to divide 10 with the given value.

Therefore,

$: \implies \bf \dfrac{5}{10} \: cm \\ \\ : \implies \bf 0.5 \: cm \\ \\ \: \: \bf \therefore \: \: Thickness = 0.5 \: cm$

Now we have,

• Surface area = 1536 cm².
• Thickness = 0.5 cm.

Now, substitute both the values in the formula of the volume of material.

$: \implies \bf 1536 \: {cm}^{2} \times 0.5 \: cm \\ \\ \\ : \implies \bf 768.0 \: {cm}^{3} \\ \\ \\ : \implies \bf 768 \: {cm}^{3} \\ \\ \: \: \bf \therefore \: \: Volume \: Of \: Material = 768 \: {cm}^{3}$

Hence,

The volume of its material whose thickness is 5 mm is 768 cm³.