Question

If each edge of cuboid of surface area 54cm^2 is double, then surface area of new cuboid is??

solve it with steps:

Answer 1

Hey Mate !

Here is your solution :

Let the dimensions of cuboid are :

Length = a

Breadth = b

Height = c

Using formula :

=> Total surface area of a cuboid = 2( lb + bh + lh )

=> 54 cm² = 2( ab + bc + ca )

=> 54 cm² ÷ 2 = ( ab + bc + ca )

=> 27 cm² = ( ab + bc + ca ) -------- ( 1 )

Now,

New length = 2a

New Breadth = 2b

New height = 2c

Using formula :

=> Total Surface area of a cuboid = 2 ( lb + bh + lh )

= 2 [ ( 2a ) ( 2b ) + ( 2b ) ( 2c ) + ( 2c ) ( 2a )]

= 2 [ 4ab + 4bc + 4ca ]

Taking out 4 as common,

= 2 × 4 [ ab + bc + ca ]

= 8 [ ab + bc + ca ]

Substituting the value of ( 1 ),

= 8 × 27 cm²

= 216 cm²


The required answer is 216 cm².

===============================

Hope it helps !! ^_^