Question

the length of the length of the diagonal of cube is 3 root 3 cm then its volume is​

Answer 1

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Answer 2

$\bold{\underline{\underline{Answer:}}}$

Volume of cube = 27 cm³

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• Length of the diagonal of a cube = 3√3 cm

To find :

• Volume of the cube

Solution :

Before we find the volume, we need to calculate the side (x) of the cube

Let the edge (side) of the cube be x cm.

We are provided with the length of the diagonal. So using the formula for diagonal of a cube we can thereby find the length of edge.

$\bold{\boxed{\red{\rm{Diagonal\:of\:a\:cube\:=\:{\sqrt{3}x}}}}}$

Block in the values,

$\rightarrow$ $\bold{3{\sqrt{3}}\:=\:{\sqrt{3}}x}$

$\rightarrow$ 3√3/√3 = x

$\rightarrow$ $\bold{3=x}$

•°• Edge of the cube = x = 3 cm

Now using the formula for volume of the cube we will get the volume too.

$\bold{\boxed{\blue{\rm{Volume\:of\:cube\:=\:x^3}}}}$

Block in the values,

$\rightarrow$ $\bold{x\times\:x\times\:x}$

$\rightarrow$ $\bold{3\times\:3\times\:3}$

$\rightarrow$ $\bold{9\times\:3}$

$\rightarrow$ $\bold{27}$

•°• Volume of the cube = 27 cm ³