Q3 of 23 Page 1

Solve sub-questions:

The length, breadth and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm2, find dimensions of the solid.

Let the Length, breadth and height of the cuboid be 5x,4x

and 2x respectively.


Total Surface Area(TSA) = (LB+BH+LH) =1216


⇒ (LB+BH+LH) = 608


⇒ [(5x × 4x) +(4x × 2x) +(5x × 2x) =608


⇒ [20x2 +8x2+10x2] =608


⇒ 38x2 = 608


⇒ x2 =


⇒ x2 = 16


⇒ x = 4


The dimension of the cuboid is:


Length = 5x= 5(4) = 20cm


Breadth = 4x=4(4) = 16cm


Height = 2x = 2(4) = 8cm


∴volume = (L×B×H)


⇒ Volume = 20 × 16 × 8


⇒ Volume = 2560cm2


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