Question

A cuboid having surface areas of 3 adjacent faces as a,b and c has the volume ?​

Answer 1

$\sqrt{abc}$

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn:- \: \star}}}}}$

A cuboid having surface areas of 3 adjacent faces as a,b and c has the volume ?

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

Volume of Cuboid = √ xyz

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

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

Now,

According to Question

Given :-

X , y and Zare areas of three adjacent faces of the cuboid.

Volume of Cuboid = ( l × b × h ) ²

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

$x \: = \: ab \: ,   \: y \: = \: bc \: , \: z \: = \: ca \\ </p><p></p><p>(x) \: (y) \: (z) \: = \: (ab)(bc)(ca) \\ </p><p></p><p>xyz \: = \: (abc)2 \\ </p><p></p><p>abc \: =  \: √xyz</p><p>$

$\huge\bold\star\pink{Thus}\star$

The volume of cuboid,

V= abc = √xyz