Question

the length of a cuboid is twice its breadth and height is twice its breadth if the volume of the cuboid is 384 cm, find its measurements

Answer 1

let the length be x cm.
then by given condition.
l=x
b=2x
h=4x
Now,
Volume of cuboid=l×b×h
384=x×2x×4x
$384 = 8 {x}^{3} \\ {x}^{3} = \frac{384}{8} \\ {x}^{3} = 48 \\ x = 3.63..$

l=3.63cm,b=7.26cm and h=12.42 cm. I hope it helps you.

Answer 2

The breadth of the cuboid is 4.579. The height and length of  of the cuboid is 9.158.

Step-by-step explanation:

Let breadth of the cuboid is x.

The length of a cuboid is twice its breadth and height is twice its breadth.

Length = 2x

Height = 2x

The volume of a cuboid is

$Volume=Length\times breadth\times height$

Volume of the cuboid is

$Volume=2x\times x\times 2x$

$Volume=4x^3$

The volume of the cuboid is 384 cm.

$4x^3=384$

Divide both sides by 4.

$x^3=96$

Taking cube root on both sides.

$x=\sqrt[3]{96}$

$x\approx 4.579$

Breadth of the cuboid is 4.579.

$2x=9.158$

Height and length of  of the cuboid is 9.158.

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