Q3 of 24 Page 164

The length, breadth, and height of a cuboid are in the ratio 6:5:3. If the total surface area is 504 cm2, find its dimension. Also, find the volume of the cuboid.

Given, length, breadth, and height of a cuboid are in the ratio 6:5:3 and the total surface area is 504 cm2.


Let length, breadth, and height of a cuboid be 6x, 5x and 3x.


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


Total Surface area of a cuboid= 504


2 × ( 6x× 5x + 5x × 3x + 3x × 6x) = 504


30x2 + 15x2 + 18x2 = 252


63x2=252



X2 =4


X=2


∴ Length = 6x = 6 × 2 =12 cm


Breadth = 5x = 5 × 2 =10 cm


Height = 3x = 3 × 2 =6 cm


We know, Volume of a cuboid= l×b×h


∴ Volume = 12×10×6


= 720 cm3


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