Question

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

Answer 1

ANSWER

Given, lateral surface area of a cube =256 m2

Lateral surface area of cube=4( edge)2

Volume of cube=( edge)3

∴4(edge)2=256

∴ edge =8

Volume of cube=(8)3=512 m3

Answer 2

Given that,

• Lateral surface area of a cube is 256 m³.

⠀

⠀$\dag\;{\underline{\frak{As \ we \ know \ that,}}}$

⠀⠀⠀

$\star\:\boxed{\sf{\pink{Lateral \ surface \ area = 4(side)^2}}}$

⠀⠀⠀⠀

And, ⠀

• we've to find out the volume of the cube.

⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀

$:\implies\sf 4(side)^2 = 256\\\\\\:\implies\sf (side)^2 = \cancel\dfrac{256}{4} \\\\\\:\implies\sf (side)^2 = 64 \\\\\\:\implies\sf side = \sqrt{64} \\\\\\:\implies{\underline{\boxed{\frak{\purple{\: side = 8 \ cm\:}}}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀

⠀$\dag\;{\underline{\frak{Formula\:of\: Volume \ of \ cube \:is\:given\:by,}}}$

⠀⠀⠀⠀

$\star\:\boxed{\sf{\pink{Volume \ of \ cube = (side)^3}}}$

⠀⠀⠀⠀

Now,

⠀⠀⠀⠀

$:\implies\sf Volume_{(cube)} = (side)^3\\\\\\:\implies\sf 8 \times 8 \times 8 \\\\\\:\implies{\underline{\boxed{\frak{\purple{\: 512 \: m^3 \: }}}}}$

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Volume \ of \ the \ cube \ is \: \bf{512 \ m^3}.}}}$