Question

The edges of the cuboid are in the ratio 1:2:3 and its surface area is 88 cm . Volume of cuboid is ?

Answer 1

let the edges be x,2x and 3x

hence

2(x.2x+2x.3x+3x.x)=88
(2x²+6x²+3x²)=44
11x²=44
x²=4
x=2

the edges are 2,4 and 6

hence volume=2*4*6
=48

Answer 2

Heya mate,Here is ur answer

Let the edges(sides) be x,2x and 3x respectively.

SA of cuboid=2(lb+bh+hl)

=2(x×2x+2x×3x+3x×x)

$88 = 2( {2x}^{2} + 6 {x}^{2} + 3 {x}^{2} )$

$88 = 2(11 {x}^{2} )$

$88 = 22 {x}^{2}$

$\frac{88}{22} = {x}^{2}$

$4 = {x}^{2}$

$\sqrt{4} = x$

2 cm = x

Then, dimensions become

x=2

2x=2×2

=4

3x=3×2

=6

Volume of a cuboid =LBH

=2×4×6
$= 48 {cm}^{3}$
Warm Regards

@ Laughterqueen

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