If the length, breadth and height of a cuboid are in ratio 3: 4: 5 and its volume is 48000cm${}^3$ then find the length, breadth and height of the cuboid.

The correct option is B

length = 60 cm, breadth = 80 cm and height = 100 cm

Given the ratio of length, breadth and height of a cuboid are in ratio 3: 4: 5 and volume is 48000cm${}^3$

$\therefore$ Let the length, breadth and height be 3$x$, 4$x$, 5$x$ respectively

$\because$ Volume of cuboid = length$\times$breadth$\times$ height

$\Rightarrow$ 3$x$ $\times$ 4$x$ $\times$ 5$x$ = 48000cm${}^3$

$\Rightarrow$ 60$x^3$ = 48000cm${}^3$

$\Rightarrow$ $x^3$ = 8000cm${}^3$

$\Rightarrow$ $x$ = 20 cm

Now the length = 3$x$

= 3 $\times$ 20cm

= 60cm

breadth = 4$x$

= 4 $\times$ 20cm

= 80cm

and height = 5$x$

= 5 $\times$ 20cm

= 100cm