Question

If the diagonal of a cube is√3/8 then its volume is​

Answer 1

Solution

Given :-

• Diagonal of cube = √3/8

Find :-

• Volume of Cube = ?

Explanation

Using Formula

$\boxed{\underline{\tt{\red{\:Diagonal_{cube}\:=\:\sqrt{3}\times (side)}}}}$

$\boxed{\underline{\tt{\red{\:Volume_{cube}\:=\:(Side)^3}}}}$

Case 1.

➡Diagonal of cube = √3/8

➡√3 × Side = √3/8

➡Side = √3/(8×√3)

➡Side = 1/8 .

Now, Calculate Volume of cube

➡Volume of cube = (Side)³

➡Volume of cube = (1/8)³

➡Volume of cube = 1/512 unit³.

Since

• Volume of cube will be = 1/512 unit³

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Answer 2

Correct Question-:

• If the diagonal of a cube is√3/8 then ,Find the volume of cube .

AnswEr -:

• $\boxed{\blue{\sf{\star{Volume \:of\:cube\:is\: \frac{1}{512}unit³}}}}$

Explanation-:

☆ Figure related to the question -:

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large side}\put(13.5,3){\bf\large side}\put(-4,5.8){\bf\large side}\end{picture}$

Given ,

• The diagonal of a cube is√3/8 unit [ Unit of the Diagonal of the cube is not given in question,]

To find ,

• Volume of a cube .

Solution -:

• $\boxed{\blue{\sf{\implies{Diagonal \: of\:cube\: = \sqrt{3} \times sides}}}}$

Here ,

• Diagonal of cube is √3/8 unit .

Now ,

• $\pink{\sf{\implies { \sqrt {3/8}\:=\sqrt{3} \times side }}}$
• $\pink{\sf{\implies { Side\:= \sqrt{3}/8 \times \sqrt{3}}}}$
• $\pink{\sf{\implies { side= \frac{1}{8} }}}$

Therefore,

• $\boxed{\purple{\sf{\star{Side\:of\:cube\:is\: \frac{1}{8}unit}}}}$...............[1]

Now ,

• $\boxed{\blue{\sf{\implies{Volume \: of\:cube\: = side \times side\times side }}}}$

Here ,

• Side of a cube is ⅛ unit ......... [ From 1]

Now ,

• $\pink{\sf{\implies { Volume\:=\frac{1}{8} \times \frac{1}{8 }\times \frac{1}{8}}}}$
• $\pink{\sf{\implies { Volume\:= \frac{1}{8} \times \frac{1}{64}}}}$
• $\pink{\sf{\implies { Volume\:=\frac{1}{512}unit³}}}$

Therefore,

• $\boxed{\purple{\sf{\implies{Volume \:=\: \frac{1}{512}unit³}}}}$

Hence ,

• $\boxed{\blue{\sf{\star{Volume \:of\:cube\:is\: \frac{1}{512}unit³}}}}$

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