Question

If the lateral surface area of a cube is 256 cm sq. , then its volume is​

Answer 1

Answer:

6

Step-by-step explanation:

6*6=36

36*6=216

answer=8

Answer 2

$\bf\huge\underline{Explanation :-}$

Given :

• Lateral surface area of cube = 256 cm²

To find :

• Volume of the cube.

Solution :

Let one side of the cube be 'x'

We know that,

$\boxed{\sf Lateral \: surface \: area \: of \: cube = 4 \times {side}^{2}}$

By putting the values,

$\sf\longrightarrow 4 \times {x}^{2} = 256$

$\sf\longrightarrow {x}^{2} = \dfrac{256}{4}$

$\sf\longrightarrow {x}^{2} = 64$

$\sf\longrightarrow x = \sqrt{64}$

$\boxed{\sf \therefore x = 8}$

Hence, one side of the cube is 8 cm.

Now, We know that,

$\boxed{\underline{\sf Volume = {x}^{3} sq.unit}}$

$\sf\longrightarrow Volume = {8}^{3} {cm}^{3}$

$\boxed{\sf \therefore Volume = 512 {cm}^{3}}$

Hence, volume of the cube is 512 cm³ respectively.

$\bf\huge\underline{More \: formulas :-}$

• Total surface area of cube = 6x² sq.unit
• Total surface area of cuboid = 2(lb + lh + bh) sq.unit
• Volume of cuboid = (l × b × h) cu.unit