The dimensions of a cuboid are in the ratio 5:3 : 1 and its total surface area is 414 m squar. find the dimension
Answers
we have given that :
the dimension ( length , breadth ,height ) are in ratio 5 :3:1
and
surface area of cuboid = 414 m²
we have to find:
length , breadth , height of cuboid = ?
solution:-
because dimension are in ratio 5 : 3:1
let :
the length of cuboid = 5x
breadth of cuboid = 3x
height of cuboid = 1x
we know that :
surface area of cuboid = 2[ lb +bh + hl ]
here,
S. area = 414
=> 2[ lb +bh + hl ] = 414
=> 2* [ 5x*3x + 3x*1x +1x*5x ] = 414 m²
=> (15x² + 3x² + 5x² ) = 207
=> 23x² = 207
=> x² = 207 / 23 = 9
=> x = 3
hence ;
the length of cuboid = 5x = 5*3 = 15m
breadth of cuboid = 3x = 3*3 = 9m
height of cuboid = x = 3m
///////////////////////////////////////////////////////////////////////////////////////////////////
@@ hope it helps @@
Answer:
Step-by-step explanation:
the dimesion of a cuboid are in the ratio 5:3:1 and its total surface area is 414m find the dimension of the cuboid
we have given that :
the dimension ( length , breadth ,height ) are in ratio 5 :3:1
and
surface area of cuboid = 414 m²
we have to find:
length , breadth , height of cuboid = ?
solution:-
because dimension are in ratio 5 : 3:1
let :
the length of cuboid = 5x
breadth of cuboid = 3x
height of cuboid = 1x
we know that :
surface area of cuboid = 2[ lb +bh + hl ]
here,
S. area = 414
=> 2[ lb +bh + hl ] = 414
=> 2* [ 5x*3x + 3x*1x +1x*5x ] = 414 m²
=> (15x² + 3x² + 5x² ) = 207
=> 23x² = 207
=> x² = 207 / 23 = 9
=> x = 3
hence ;
the length of cuboid = 5x = 5*3 = 15m
breadth of cuboid = 3x = 3*3 = 9m
height of cuboid = x = 3m