Question

The surface area of a cuboid is 1872m^2 . If its length,breadth and height are in the ratio 4:3:2, find its volume

Answer 1

Let the length be 4x, breadth be 3x and height be 2x, as their ratios is 4 : 3 : 2


We know that surface area of cuboid
= 2(lb + bh + lh)


So surface area =
$2(4x \times 3x + 4x \times 2x + 2x \times 3x)$

=> Surface area =
$2(12 {x}^{2} + {8x}^{2} + {6x}^{2} ) \\ \\ = > 2(26 {x}^{2} ) \\ \\ = > 52 {x}^{2}$

Now given that surface area = 1872

=> 52x² = 1872

=> x² = 1872/52

=> x² = 36

=> x = √36

=> x = ±6

Since length can't be negative, we take x = 6

So length = 4x = 4(6) = 24 m
Breadth = 3x = 3(6) = 18 m
Height = 2x = 2(6) = 12 m


So, Volume = Length × Breadth × Height

=> Volume = 24 × 18 × 12

=> Volume = 5184 m³

Answer :- 5184 m³