NIELIT 2021 Dec Scientist A - Section A: 38

Question

The length, breadth and height of a cuboid are in the ratio $3 : 4 : 5$ and its volume is $3840 \; \text{cm}^{3},$ The smallest side has a length of :

• A. $12 \; \text{cm}$
• B. $20 \; \text{cm}$
• C. $15 \; \text{cm}$
• D. $18 \; \text{cm}$

Answer 1

Let’s assume that the length, breadth, and height of a cuboid is $3x,4x,5x.$

$\because$ Volume of cuboid =Lenght*breadth*hight

$\therefore$ Volume of cuboid= $3840 \ cm^2$

$\implies 3840 =3x*4x*5x$

$\implies 3840=60x^3$

$\implies x^3=\frac{3840}{60}$

$\implies x^3=64$

$\implies x=64^\frac{1}{3}$

$\implies x=4$

$\therefore $ Smallest side has length = $3x=3*4=12$ cm

Option $(A)$ is correct.