Question

The dimensions of a cuboid are in the ratio 2 : 3 : 4 and its total surface area is 3328

cm2

. Find the dimensions of this cuboid.

Answer 1

The dimensions of cuboid are given in the ratio

Let the ratio be 2x : 3x : 4x

The TSA = 3328cm²

2 ( lb + bh + hl ) = 3328

2 ( 2x × 3x + 3x × 4x + 4x × 2x) = 3328

6x² + 12x² + 8x² = 1664

26x² = 1664

x² = 1664 / 26

x² = 64

x = √64

x = 8cm.

the dimensions of cuboid are :

2x = 2 × 8 = 16
3x = 3 × 8 = 24
4x = 4 × 8 = 32.

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Answer 2

Let the ratio of the sides of the cuboid be 2x:3x:4x

Now TSA=3328 (given)

TSA OF CUBOID=2 (lb+bh+hl)
3328=2 (2x.3x+3x.4x+4x.2x)
3328/2=(6x^2+12x^2+8x^2)
1664=26x^2
x^2=1664/26
x^2=64
x=8
now therefore dimensions of cuboid
=> 2x=2×8=16cm
=> 3x=3×8=24cm
=> 4x=4×8=32cm

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