Question

the diagnol of a cube is
$\sqrt{12}$
find its volume​

Answer 1

$\mathtt{ \underline{ \huge \purple{ \fbox{ \orange{ \: Solution \: \: \red: }}}}}$

Given ,

The diagonal of cube = √12 units

We know that , the diagonal of cube is given by

$\star \: \large \sf \fbox{Diagonal \: of \: cube = \sqrt{3} \times side }$

Substitute the values , we get

$\sf \hookrightarrow \sqrt{12} = \sqrt{3} \times side$

Squaring both sides , we obtain

$\sf \hookrightarrow 12 = 3 \times {(side)}^{2} \\ \\ \sf \hookrightarrow {( side )}^{2} = 4 \\ \\ \sf \hookrightarrow side = 2 \: \: units$

Now , the volume of cube is given by

$\sf\large \fbox{Volume \: of \: cube = {(side)}^{3} }$

Substitute the values , we obtain

$\sf \hookrightarrow Volume = {(2)}^{3} \\ \\\sf \hookrightarrow Volume = 8 \: \: {units}^{3}$

Hence , the volume of cube is 8 units³

Answer 2

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