Question
The total surface area of a cube is $864 \ cm^2$. Find its volume.
✓
Answer
Let the side of the cube be ' $a$ ' $cm$
$\therefore$ Total surface area of a cube $=6 a^2$
$ \therefore 864=6 a^2 \ldots($Given$)$
$a^2=\frac{864}{6}$
$a^2=144$
$a=\sqrt{144} \ldots ($Taking square roots on both sides$)$
$\therefore a=12 \ cm $
$...($Given$)$
$a=\sqrt{144} \ldots ($Taking square roots on both sides$)$
$\therefore a=12 \ cm$
Volume of a cube
$ =a^3$
$=12^3$
$=1728 \ cm ^3 $
$\therefore$ Volume of the cube $=1728 \ cm ^3$.
$\therefore$ Total surface area of a cube $=6 a^2$
$ \therefore 864=6 a^2 \ldots($Given$)$
$a^2=\frac{864}{6}$
$a^2=144$
$a=\sqrt{144} \ldots ($Taking square roots on both sides$)$
$\therefore a=12 \ cm $
$...($Given$)$
$a=\sqrt{144} \ldots ($Taking square roots on both sides$)$
$\therefore a=12 \ cm$
Volume of a cube
$ =a^3$
$=12^3$
$=1728 \ cm ^3 $
$\therefore$ Volume of the cube $=1728 \ cm ^3$.
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