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

$256 m^{3}$

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$512 m^{3}$

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$64 m^{3}$

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$128 m^{3}$

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Solution

The correct option is B
$512 m^{3}$

Lateral surface area of cube
$= 4 (edge)^{2}$

$∴ 4 (edge)^{2} = 256 m^{2}$

$\Rightarrow (edge)^{2} = \frac{256}{4}$

$\Rightarrow (edge)^{2} = 64$

$\Rightarrow edge = \sqrt{64} = 8 m$

$Volume of cube = (edge)^{3}$
$= (8)^{3}$
$= 512 m^{3}$

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The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is:

A) $512 m^{3}$
B) $64 m^{3}$
C) $216 m^{3}$
D) $256 m^{3}$

Q. The lateral surface area of a cube is

256

^{2}

. The volume of the cube is:

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

Q. A lateral surface area of cube is

256 m^{2}

. find its volume

Q. The lateral surface area of a cube is 256 m². The volume of the cube is
(a) 64 m³
(b) 216 m³
(c) 256 m³
(d) 512 m³

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

The correct option is B 512 m3 Lateral surface area of cube =4(edge)2 ∴ 4(edge)2=256 m2 ⇒(edge)2=2564 ⇒(edge)2=64 ⇒edge=√64=8 m Volume of cube=(edge)3 =(8)3 =512 m3

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

The correct option is B
$512 m^{3}$

Lateral surface area of cube
$= 4 (edge)^{2}$

$∴ 4 (edge)^{2} = 256 m^{2}$

$\Rightarrow (edge)^{2} = \frac{256}{4}$

$\Rightarrow (edge)^{2} = 64$

$\Rightarrow edge = \sqrt{64} = 8 m$

$Volume of cube = (edge)^{3}$
$= (8)^{3}$
$= 512 m^{3}$