Question

12. The surface area of a cube is 24 cm².

(i) Find the length of its edge.
(ii) Find its volume.

Answer 1

Given :-

surface area of a cube is 24 cm².

To find :-

➡Edge length = ?

➡ volume = ?

Formula used

Total Surface Area = 6(edge)²

Volume of cube = (edge)³

Solution:-

i) surface area of a cube is 24 cm²

⇒ 6(edge)² = 24

⇒ (edge)² = 24/6

⇒ (edge)² = 4

⇒ (edge) = √4 = + 2 ( as edge length cannot be negative)

Hence, edge of the cube is 2 cm

ii) volume = ?

volume= (edge)³

volume = (2)³

volume = 8 cm³

Hense, volume of the cube is 8cm³

Additional information--

• Cube: A cube is a three-dimensional shape that is defined in the XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are square in shape and have equal dimensions.

Formulae:-

Cube:-

• Total Surface Area = 6(edge)²
• Lateral Surface Area = 4 (edge)²
• Volume of cube = (edge)³
• Diagonal of a cube = √3(edge)
• Perimeter of cube = 12 × edge.

Answer 2

`\large \:\sf \underline{Explanation.}`

`\sf{\underline{Given}}`

• 
  `\sf \: surface \: area \: = \: 24 {cm}^(2)`

`\sf{\underline{Formula}}`

• TSA = 6a²
• Volume = a³

`\sf \: {Let's \: Begin}`

(i) Find the length of its edge.

Let edge = x

We know that,

TSA of cube = 6a²

6a² = 24

a² = 24/6

a² = 4

a = √ 4 { Ignore negative value}

a = 2

`\bf \pink{length \: of \: edge \: \: = \: 2 \: cm}`

(ii) Find its volume.

We know that,

(2)³

= 8

`\bf \green{volume \: = \: 8 \: cm {}^(3) }`

Thus ,

1. Edge = 2 cm
2. Volume = 8 cm³

`\red {\rule{ \170pt}{4pt}}`