Question

The area of three adjacent faces of cuboid is x,y,z its volume is

1. V=xyz

2.V^3=xyz

3.V^2=xyz

4.none of these

Answer 1

3) V² = xyz

Hope this answer helps you.

Answer 2

Answer:

( 3 ) V² = xyz

Step-by-step explanation:

Given----> Area of three adjacent faces of cuboid are x , y and z .

To find---> Volume of cuboid

Solution---> We know that faces of cuboid are treated as rectangles and

Area of rectangle = Product of its dimensions

Now three faces of cuboid are adjacent so , dimension of one face are length and breadth , dimension of other face is length and height and dimension of remaining adjacent face is breadth and height

Now , let area of first , second and third adjacent faces are x , y ,and z respectively.So,

x = length × breadth

x = l × b

y = length × height

y = l × h

z = breadth × height

z = b × h

Now ,

x y z = ( l b ) ( l h ) ( b h )

= l² b² h²

x y z = ( l b h )²

Taking square root of both sides , we get,

=> √( x y z ) = l b h

We know that ,

Volume of cuboid = l b h

=> V = l b h , Putting it above , we get,

=> √(x y z ) = V

=> V = √( xyz )

Squaring both sides we get,

=> V² = ( √xyz )²

=> V² = xyz

Answer is ( 3 ) V² = xyz

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