Question

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

• A. length = 80 cm, breadth = 60 cm and height = 100 cm
• B. length = 30 cm, breadth = 40 cm and height = 40 cm
• C. length = 120 cm, breadth = 40 cm and height = 10 cm
• D. length = 60 cm, breadth = 80 cm and height = 80 cm

Answer 1

The correct option is B

length = 30 cm, breadth = 40 cm and height = 40 cm

Given: The ratio of length, breadth and height of a cuboid= 3: 4: 4 and volume is 48000cm${}^3$

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

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

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

$\Rightarrow$ 48$x^3$ = 48000cm${}^3$

$\Rightarrow$ $x^3$ = 1000cm${}^3$

$\Rightarrow$ $x$ = 10 cm

Now the length = 3$x$

= 3 $\times$ 10cm

= 30cm

breadth = 4$x$

= 4 $\times$ 10cm

= 40cm

and height = 4$x$

= 4 $\times$ 10cm

= 40cm