Question

The length, breadth and height of a cuboid are in the ratio 5:3:2. If its volume is 35.937 m³, find its dimension. Also find the total surface area of the cuboid.

Answer 1

It is given that the ratio of length, breadth and height of the cuboid is 5 : 3 : 2 and the volume of the cuboid is 35.937 m³.


Let the length of the cuboid is 5 a,
Breadth of the cuboid is 3 a,
Height of the cuboid is 2 a,




From the properties of cuboid, we know : -

Volume of cuboid = length x breadth x height.


Then,

= > 5 a x 2 a x 3 a = 35.937 m³

= > 30 a³ = 35.937 m³

= > a³ = 1.1979 m³

= > a = 1.06204 ---: ( 1 )



From the properties of cuboid, we know : - Total surface area = 2[ lb + bh + hl ], where l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.


Therefore,
Total surface area = 2[( 5a x 3a ) + ( 3a x 2a ) + ( 2a x 5a ) ]

Total surface area = 2[ 15a² + 6a² + 10a² ]

Total surface area = 2 x 31a²

Total surface area = 62a²


Now, substituting the value of a from ( i ),

Total surface area = 62( 1.06204 m )²

Total surfaces area = 62 x 1.12793 m²

Total surface area = 69.93137 m²




Hence,
Total surface area of the cuboid is 69.93137 m²
$\:$

Answer 2

Solution :

Let l , b and h are length , breadth and

height of a cuboid respectively ,

l : b : h = 5 : 3 : 2 [ given ]

Let l = 5x m ,

b = 3x m ,

h = 2x m ,

Volume ( V ) = 35.937 m³

=> l * b * h = 35.937 m³

=> (5x) * ( 3x ) * ( 2x ) = 35.937

=> 30x³ = 35.937

=> x³ = 35.937/30

=> x³ = 1.1979

=> x = ( 1.1979 )^⅓

=> x ≈ 1.06

Now ,

l = 5x = 5 × 1.06 = 5.3 m

b = 3x = 3 × 1.06 = 3.18m

h = 2x = 2 × 1.06 = 2.12m

Total Surface Area = 2( lb + bh + hl )

= 2[ 5.3×3.18+3.18×2.12+2.12×5.3 ]

= 2( 16.854 + 6.7416+11.236)

= 2 × 34.8316

= 69.6632 m²

≈ 69.67 m²

••••