Question

) The surface area of a cube is 256 sq m., the volume of the cube is
(a) 64 cubic metre (b)216 cubic metre (c) 256 cubic metre (d) 512 cubic meter.( Hint: The number of surfaces is 6)
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Answer 1

Correct Question :-

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

• 64 cubic metre
• 216 cubic metre
• 256 cubic metre
• 512 cubic meter. (Ans.)

( Hint: The number of surfaces in cube is 6)

Answer :-

• Volume of cube =

Given :-

• LSA of cube = 256 m²

To Find :-

• Volume of cube = ?

Explanation :-

As we know, to we have the LSA of cube and we need to find the volume of cube. In order to find the volume of the cube first we need to find the side of the cube.

Let the side of the cube to be 'x' m

$\green { \boxed { \bf \bigstar \; LSA \; of \; cube = 4 \; (Side)^2 \; \bigstar }}$

$\rm : \longrightarrow 4 \; (x)^2 = 256 \; \; m^2$

$\rm : \longrightarrow (x)^2 = \dfrac{256}{4} \; \; m^2$

$\rm : \longrightarrow (x)^2 = 64 \; \; m^2$

$\rm : \longrightarrow x = \sqrt{64} \; \; m^2$

$\blue { \underline { \boxed { \bf : \longrightarrow x = 8 \; \; m }}}$

Hence, the side of the cube is 8 m.

Now Finding the volume,

$\purple { \boxed { \bf \bigstar \; Volume ]; of \; cube = (Side)^3 \; \bigstar }}$

$\rm : \longrightarrow (Side)^3 \; \; m^3$

$\rm : \longrightarrow (8)^3 \; \; m^3$

$\rm : \longrightarrow 8 \times 8 \times 8 \; \; m^3$

$\rm : \longrightarrow 64 \times 8 \; \; m^3$

$\red { \underline { \boxed { \bf : \longrightarrow 512 \; \; m^3 \qquad \star }}}$

Hence, the volume of the cube id 512 m³. (Option D)