Question

The lateral surface area of a cube is 256 m². The volume of the cube is

A.
512 m³

B.
64 m³

C.
216 m³

D.
256 m³​

Answer 1

Answer:

512

Step-by-step explanation:

Here is your answer

Answer 2

Answer:

Given :

$\sf{Lateral\: surface\: area\: of \:the \;cube = {256}^{2}}$

To find :

$\textsf{The volume of the cube}$

Concept :

To find the volume of the cube first find the edge of the cube .

Use this formula to find the edge of the cube :

$\sf\boxed{E={a}^{\dfrac{1}{3}}}$

Where,

E = Edge

a = Surface area

Now , to find the volume of the cube use this formula :

$\sf\boxed{V={E}^{3}}$

Where,

V = Volume

E = Edge

So , edge is -:

$\sf:\implies{E={({256m}^{2})}^{\dfrac{1}{3}}}$

$\sf:\implies{E=6.5m}$

So , the edge is 6.5 m .

Solution :

$\sf:\implies{V={6.5m}^{3}}$

$\sf:\implies{V=6.5\times6.5\times6.5}$

$\sf:\implies{V=42.25\times6.5}$

$\sf:\implies{V={274.62500m}^{3}}$

So , the volume of the cube is $\sf{{274.62500m}^{3}}$

Answer :

Volume of the cube = $\sf{{274.62500m}^{3}}$