Question

the surface area of a cube is 384 cm2 . what will be it's volume​

Answer 1

• Volume of cube is 512 cm³.

Step-by-step explanation:

To find:-

• Volume of cube.

Solution:-

Given that,

Surface area of cube is 384 cm².

• First we will find edge of cube for volume of cube.

Surface area of cube = 6a²

• Here, a is edge of cube.

➝ 6 a² = 384

➝ a² = 384/6

➝ a² = 64

➝ a = √64

➝ a = 8

a is edge of cube. So, Edge of cube is 8 cm.

Now, According to question.

Volume of cube = a³

➝ 8 × 8 × 8

➝ 512

Therefore,

Volume of cube is 512 cm³.

Answer 2

Given:-

The surface area of a cube is 384 cm².

To Find :-

What is the volume of cube.

Formula Used :-

❶ Surface area of cube,

$\boxed{\bold{\small{Total\: Surface\: Area\: Of\: Cube\: =\: {6a}^{2}}}}$

❷ Volume of cube,

$\boxed{\bold{\small{Volume\: Of\: Cube\: =\: {a}^{3}}}}$

Solution :-

Given :

The surface area of a cube is 384 cm².

❶ First we have to find the surface area of cube,

✦ Total Surface area of cube = 6a²

⇒ 6a² = 384

⇒ a² = $\sf\dfrac{\cancel{384}}{\cancel{6}}$

⇒ a² = 64

⇒ a = $\sqrt{64}$

⇒ a = 8 cm

Hence, the T.S.A of the cube is 8 cm

❷ Now, we have to find the value of volume of cube,

⇒ Volume = a³

⇒ Volume = (8)³

$\Rightarrow$ Volume = 512 cm²

$\therefore$ The volume of cube is 512 cm² .

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