Question

9. The areas of three faces of a cuboid which meet at one of the vertices are X, Y and Z. Find the volume of the cuboid. ​

Answer 1

solution

Let the sides of the cuboid be a, b & c.

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc)

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc=

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz ∴ volume of cuboid =

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz ∴ volume of cuboid = xyz

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz ∴ volume of cuboid = xyz

Let the sides of the cuboid be a, b & c.Given x, y & z are areas of 3 adjacent faces of the cuboid.Hence x=ab, y=bc, z=ca(x)(y)(z)=(ab)(bc)(ca)xyz=(abc) 2 ⇒abc= xyz ∴ volume of cuboid = xyz

Answer 2

Answer:

the areas of three faces of a cuboid which meet at one of the vertices are x,y and z. find the volume of the cuboid