Question

the lateral surface area of the cube is 256 cubic cm find volume ​

Answer 1

lateral surface area =256

$256=4a^2\\a^2=\frac{256}{4}\\a^2=64\\a=\sqrt64\\a=8$

volume of cube=$a^3$

$8^3\\8×8×8\\512cm^3$

Answer 2

Given:-

• surface area of cube is 256 cm²

To Find:-

• Volume of cube?

Solution:-

Formula to find Surface area of cube

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

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.