Question

the surface area of 3 adjacent faces of a cube are x,y,,z respectively find the volume of cube

Answer 1

Hey

• Let the length be = l

• Let the breadth be = b

• Let the height be = h

Now area of base = l * b

= lb –––– ( i )

Area of it's adjacent side

= bh –––– ( ii )

Area of one of it's adjacent side

= lh –––– ( iii )

Now ,

Eq ( i ) * eq ( ii ) * eq ( iii )

= lb * bh * lh

= l ² * b ² * h ² .

Also given that areas are :- x , y , and z respectively .

So

l ² * b ² * h ² = xyz

=> ( l b h ) ² = xyz

=> l b h = √ xyz

And we know that

volume = l b h

So volume = √ xyz .


thanks :)