The dimensions of a box are in the ratio of 5: 2: 4 and its total surface area is 304 m2. Find the volume of box.
320 m3
Let the proportional constant be x
Length of box be 5x
Breadth of box be 2x
Height of box be 4x
By formula, surface area of cuboid = 2(lb + bh + lh)
2(5x.2x + 2x.4x + 5x.4x) = 304 m2
(10 x2 + 8 x2 + 20 x2) = 152 m2
38 x2 = 152 m2
x = √4m2
x = 2 m
Now, length of box = 5x = 5 × 2 = 10 m
Breadth of box = 2x = 2 × 2 = 4 m
Height of box = 4x = 4 × 2 = 8 m
So, volume of box = lbh
= 10 m × 4 m × 8 m
= 320 m3