Question

What is the volume of a cube whose diagonal is 8√3cm long?​

Answer 1

Here ,

Given

•diagonal of cube =8√3cm

Let side of the cube be x cm

$diagonal \: of \: cube = \sqrt{3} x \\ = > 8 \sqrt{3} = \sqrt{3} x$

here √3 get cancel out

so , x = 8cm = side of the cube

Now , volume of cube =x^3

$= > {8}^{3} \\ = > 8 \times 8 \times 8 \\ = > 512cm ^{3}$

hence , the volume of the cube is

$\boxed{512cm ^{3} }$

Answer 2

$\huge{\red{\underline{\rm{Solution:}}}}$

$\underline{\sf{Let\;side\;of\;cube\;be\;a\;units.}}$

${\blue{\underline{\sf{Given:}}}}$

$\sf{\implies Diagonal\;of\;cube=8\sqrt{3}\;cm}$

${\blue{\underline{\sf{To\;Find:}}}}$

$\sf{\implies Volume\;of\;cube.}$

${\blue{\underline{\sf{Formula\;used:}}}}$

$\sf{\implies Diagonal\;of\;cube=\sqrt{3} a}$

$\sf{\implies Volume\;of\;cube=a^{3}}$

$\underline{\sf{Now,\;we\;will\;put\;the\;values\;in\;the\;formula,}}$

$\sf{\implies Diagonal\;of\;cube=\sqrt{3} a}$

$\sf{\implies 8\sqrt{3}=\sqrt{3} a}$

$\sf{\implies a=8\;units}$

$\underline{\sf{Now,\;we\;will\;calculate\;volume.}}$

$\sf{\implies Volume\;of\;cube=a^{3}}$

$\sf{\implies Volume\;of\;cube=(8)^{3}}$

$\sf{\implies Volume\;of\;cube=512\;cm^{3}}$

$\large{\boxed{\boxed{\red{\sf{Hence,\;Volume\;of\;cube=512\;cm^{3}}}}}}$