Question

the length,breadth,and height of a cuboid are in the ratio 5:3:2,and its total surface area is 3,968cm2 .find the dimension of the cuboid ​

Answer 1

Answer:

Step-by-step explanation:

TSA of cuboid = 2 [lb + bh + lh]

ratio of dimension = 5:3:2

so, let the dimensions be 5x, 3x and 2x

TSA of cuboid = 2 [lb + bh + lh] = 3968

= 2 [5x × 3x + 3x × 2x + 5x × 2x] = 3968

= 2 [15x + 6x + 10x] = 3968

= 2 × 31x = 3968

= 31x =  3968/2

= 31x =  1984

= x = 1984/31

= x = 64

∴ length = 5x = 5 × 64 = 320 cm

  breadth = 3x = 3 × 64 = 192 cm

  height = 2x = 2 × 64 = 128 cm

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