Q6 of 24 Page 164

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.

Given, length, breadth, and height of a cuboid are in the ratio 5:3:2 and its volume is 35.937 m3.


Let length, breadth, and height be 5x, 3x and 2x.


We know, Volume of a cuboid= l×b×h


∴ Volume = l×b×h


35.937 = 5x × 3x × 2x


35.937 = 30x3



X3=1.1979


X= 1.06 m


∴ Length = 5x = 5 × 1.06 = 5.3 m


Breadth = 3x = 3 × 1.06 =3.18 m


Height = 2x = 2 × 1.06 = 2.12 m


We know, Total Surface area of a cuboid= 2 × (lb + bh+ hl).


∴ Total Surface area of a cuboid= 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


= 69.66 m2


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