Question

If a lateral surface area of a cube is 256 CM square then find the volume of the cube

Answer 1

In it 6πr^2 =256

πr^2=128/3
R^2=64*7/11*3
R =8√7/√33

So volume is πr^3

Pit value of r and find volume

Answer 2

Given:-

• surface area of cube is 256 cm²

To Find:-

• Volume of cube?

Solution:-

Formula to find Surface area of cube

$\dag{ \underline{ \boxed{ \rm{ \pink{6 {a}^{2} }}}}}$

Where,

• a = side

Breadth of cube

$\longrightarrow \: 6 {a}^{2} = {256}^{2} \\ \\ \longrightarrow \frac{256}{6} = {a}^{2} \\ \\ \longrightarrow 4.41 = {a}^{2} \\ \\ \longrightarrow \sqrt{4.41} =a \\ \\ \longrightarrow \dag { \underline{ \boxed{ \rm{ \green{2.1 = a}}}}}$

Formula to find volume of cube

$\dag{ \underline{ \boxed{ \rm{ \blue{ {side}^{3} }}}}}$

Now, volume of cube

$\longrightarrow {2.1}^{3} \\ \\\longrightarrow 2.1 \times 2.1 \times 2.1 \\ \\ \longrightarrow \dag { \underline{ \boxed{ \rm{ \green {{9.261 \: cm}^{3} }}}}}$

Hence, the measure volume of cube is 9.261 cm³.