Question

The length, breadth, and height of a cuboid are in the ratio 5:3:2, and its total area is 3968 cm^2. Find the dimensions of the cuboid.​

Answer 1

Let the dimensions be 5x, 3x and 2x.

Now,

2(lb + bh + hl) = Total surface area

=> 2( 5x × 3x + 3x × 2x + 2x × 5x ) = 3968 cm²

=> 2( 15x² + 6x² + 10x² ) = 3968 cm²

=> 2(31x²) = 3968 cm²

=> 62x² = 3968 cm²

=> x² = 3968

62

=> x² = 64

=> x = √64

=> x = 8

Therefore,

length = 5x = 5×8 = 40 cm

breadth = 3x = 3×8 = 24 cm

height = 2x = 2×8 = 16 cm

Answer 2

Given :

The length breadth and height of a cuboid are in the ratio 5:3:2 .

Total Surface Area is 3968 cm² .

To Find :

Dimensions of the cuboid .

Solution :

$\longmapsto\tt{Let\:Length\:be=5x}$

$\longmapsto\tt{Let\:Breadth\:be=3x}$

$\longmapsto\tt{Let\:Height\:be=2x}$

Using Formula :

$\longmapsto\tt\boxed{S.A\:of\:Cuboid=2(lb+bh+hl)}$

Putting Values :

$\longmapsto\tt{3968=2(5x\times{3x}+3x\times{2x}+2x\times{5x})}$

$\longmapsto\tt{3968=2({15x}^{2}+{6x}^{2}+{10x}^{2})}$

$\longmapsto\tt{\cancel\dfrac{3968}{2}={31x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{1984}{31}={x}^{2}}$

$\longmapsto\tt{\sqrt{64}=x}$

$\longmapsto\tt\bf{8=x}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Length\:of\:Cuboid=5(8)}$

$\longmapsto\tt\bf{40\:cm}$

$\longmapsto\tt{Breadth\:of\:Cuboid=3(8)}$

$\longmapsto\tt\bf{24\:cm}$

$\longmapsto\tt{Height\:of\:Cuboid=2(8)}$

$\longmapsto\tt\bf{16\:cm}$