Question

Length breadth ; height of a cuboid are in ratio 2:3:4.if the surface area is 520cm square . find the volume of a cuboid

Answer 1

volume of a cuboid is 758.94 cm³ .

Step-by-step explanation:

formula used :

Volume of cuboid = length × breadth × height  ................. eq 1

SA of cuboid =2 ( length × breadth) + 2 ( breadth × height ) +2(length ×  height )  .................... eq 2

let

l be the length ;

h be the height ;

b be the breadth ;

given that :

l:b:h = 2:3:4

let  l = 2 K , b = 3k ; h = 4 K  where K is a constant  ....................eq 3  

// introduction of k doesnot make any difference as the ratio of l:b:h doesnot make any difference ,

SA of cuboid =2lb+2lh+2hb,

2lb+2lh+2hb  = 520  ................eq 4

using eq 3 in eq 4

2 { 2K*3K + 3K*4K + 4K*2K } = 520

2{ 6K² + 12K²+8K² }    = 520

26 K² = 260

K² = 10  

K = $\sqrt{10}$

NOW

l = 2$\sqrt{10}$

b = 3$\sqrt{10}$

h = 4$\sqrt{10}$

volume of cuboid = l*b*h

                          = 2$\sqrt{10}$  *3$\sqrt{10}$ *  4$\sqrt{10}$  

                          = 240$\sqrt{10}$

                          = 758.94 cm³