Question

The volume of a cube of $60$ cm side is the same as that of a cuboid one of whose sides is $36$ cm If the ratio of the other two sides is $15:16.$Then the largest side of the cuboid is :

• A. $60$ cm
• B. $75$ cm
• C. $80$ cm
• D. $90$ cm

Answer 1

Answer: (C)

$80$ cm

Side of cube$=60cm$

Volume of cube$={\left(60\right)}^3=216000c{m}^3$

Let $l=36cm,b=15x,h=16x$

Now, $lbh=21600\Rightarrow 36\times 15x\times 16x=21600$

$\Rightarrow x^2=\frac{21600}{36\times 15\times 16}=\frac{400}{16}=25$

$\Rightarrow x=\sqrt{25}=5$

$\therefore b=15\times 5=75cm,h=16\times 5=80cm$

$\therefore$Largest side of cuboid$=80cm$